RMR Prediction

Load Data

Load Enable Data

library(readxl)
library(tidytable)

## 
## Attaching package: 'tidytable'

## The following objects are masked from 'package:stats':
## 
##     dt, filter, lag

## The following object is masked from 'package:base':
## 
##     %in%

conflicted::conflict_prefer_all('tidytable', quiet = TRUE)
data_folder <- "data"

# load enable data
enable_data <- read_xlsx(file.path(data_folder, "enable_Datensatz_RMR._Erwachsene 1.xlsx"), skip = 2, na=c('NA', 'N/A', ''))

# fix compound values
compounds <- c(
  "acetic acid a", "butyric acid a", "propionic acid a",
  "2-Methylbutyrate a", "hexanoic acid c", "Isobutyrate a",
  "Isovalerate a", "pentanoic acid a",
  "4-Methylvaleric acid a", "Lactic acid a"
)

# for all columns that have a comma in their name, replace commas in the column with a dot
for (column_name in names(enable_data)) {
  if (is.character(enable_data[[column_name]])) {
    enable_data[[column_name]] <-
      sub(",", ".", enable_data[[column_name]], fixed = TRUE)
    # for compounds, replace "<0" with 0 to be able to convert to numeric
    if (column_name %in% compounds) {
      # replace "<0" with 0
      enable_data[[column_name]] <-
        ifelse(enable_data[[column_name]] == "<0" |
                 enable_data[[column_name]] == "< 0", 0, enable_data[[column_name]])
    }
  }
}

# write to csv and read again using fread to get the correct data types
data_csv <- file.path(data_folder, 'enable_data.tsv')
fwrite(enable_data, file = data_csv)
enable_data <- data.table::fread(data_csv, stringsAsFactors = TRUE, na=c('NA', 'N/A', ''))

# add 1 to the weight of the nuernberg site
enable_data[Site == "nuernber", `GEWICHt_SECA, kg` := `GEWICHt_SECA, kg` + 1]

enable_data[Site == "nuernber", Site := "Nuremberg"]
enable_data[Site == "freising", Site := "Freising"]

# remove unnecessary column:
if(all(enable_data[, `Probanden-ID` == Label]))
  invisible(enable_data[, `Probanden-ID` := NULL])

Load Microbiome Data

# load microbiome mapping
microbiome_mapping <- data.table::setDT(read_xlsx(file.path(data_folder, "mapping_file 1.xlsx")))
microbiome_mapping[, sample_clean := data.table::tstrsplit(".", x = `#SampleID`, fixed = TRUE, keep = 2)]
# check uniqueness
stopifnot(!any(microbiome_mapping[, duplicated(sample_clean)]))

# load microbiome data
microbiome_data <- fread(file.path(data_folder, "tax.summary.all 1.tab"))
stripped_names <- unlist(data.table::tstrsplit(".", x = names(microbiome_data), fixed = TRUE, keep = 2))
# check uniqueness
stopifnot(!any(duplicated(stripped_names)))
# clean names
names(microbiome_data) <- stripped_names
# get taxa names
taxa_names <- microbiome_data[, V1]
# transpose data
microbiome_data <- microbiome_data |> data.table::transpose(keep.names = "sample_clean", make.names = "V1")
# merge microbiome data with mapping
microbiome_data[microbiome_mapping, on=.(sample_clean), c("Label", "Cohort"):=.(Code, as.character(Cohort))]
# merge with enable data
invisible(enable_data[microbiome_data, on=.(Label), (c(taxa_names, "Cohort")) := mget(c(taxa_names, "Cohort"))])
# create field for first letter of label, i.e., categorical Age and Site
invisible(enable_data[, Label_group:=substr(Label, 1, 1)])

Add Alpha Diversity

# diversity columns
diversity_columns <- c("Shannon.effective", "Simpson.effective")
# load diversity data
diversity_data <- fread('data/Final table.tab', stringsAsFactors=TRUE) |> data.table::setnames(old='V1', new="Label") |> select(Label, all_of(diversity_columns))

invisible(enable_data[diversity_data, on=.(Label), (c(diversity_columns)) := mget(diversity_columns)])

Set Variable Groups

name_mapping <- c(
  "SEX" = "Sex",
  "Alter, Jahre" = "Age",
  "mean_temp" = "Mean Outdoor Temperature",
  "Datum_V1" = "Date",
  "GROESSE, cm" = "Height",
  "GEWICHt_SECA, kg" = "Weight",
  "FETTMASSE_SECA, kg" = "FM",
  "FFM_SECA,kg" = "FFM",
  "VISZFETT,l" = "Visceral Fat",
  "TAILLENUMFANG,cm" = "Waist",
  "HUEFTUMFANG, cm" = "Hip",
  "Körpertemperatur, °C" = "Body Temperature",
  "RMR.KJ" = "RMR",
  "LEUKOZYTEN/nl" = "Leukocytes",
  "hsCRP, mg/dl" = "hsCRP",
  "INSULIN, µU/ml" = "Insulin",
  "TSH, µU/ml" = "TSH",
  "FT3, pg/ml" = "fT3",
  "Hämoglobin, g/dl" = "Hemoglobin",
  "Hämatokrit, %" = "Hematocrit",
  "MCHC, g/dl" = "MCHC",
  "GOTAST, U/l" = "GOT AST",
  "GPTALT, U/l" = "GPT ALT",
  "GGT, U/l" = "GGT",
  "LDH, U/l" = "LDH",
  "Blutzucker, mg/dl" = "Glucose",
  "Cholesterin, , mg/dl" = "Cholesterol",
  "Triglyzeride, mg/dl" = "Triglycerides",
  "HDLCHOL, mg/dl" = "HDL",
  "LDLCHOL, mg/dl" = "LDL",
  "KREATIN, mg/dl" = "Creatinine",
  "GFRCKDE, mg/min" = "GFR",
  "HARNSTOFF, mg/dl" = "Urea",
  "Harnsäure, mg/dl" = "Uric Acid",
  "EISEN,µg/dl" = "Iron",
  "FERRITIN,ng/ml" = "Ferritin",
  "Blutdruck_systolisch, mmHg" = "BP Systolic",
  "Blutdruck_diastolisch, mmHg" = "BP Diastolic",
  "Herzfrequenz, Schläge pro Minute" = "Heart Rate"
)

data.table::setnames(enable_data, old = names(name_mapping), new = name_mapping)

# groups for taxa
taxa_group <-
  c(
    k = 'kingdom',
    p = 'phylum',
    c = 'class',
    o = 'order',
    f = 'family',
    g = 'genus'
  )[data.table::tstrsplit(taxa_names,
                          split = '__',
                          keep = 1,
                          fixed = TRUE)[[1]]]
# match the columns to certain groups
column_groups <- rbind(data.table::data.table(column = 'Label_group', group = "General information"),
                       fread(file.path(data_folder, 'column_groups.tsv')),
                       data.table::data.table(column = taxa_names, group = paste("microbiome", taxa_group)),
                       data.table::data.table(column = diversity_columns, group = paste("microbiome diversity")))
column_groups[, group:=as.factor(group)]
column_groups[column %in% names(name_mapping), column := name_mapping[column]]

# set general response variable
response_variable <- "RMR"
# Conversion factor kcal to kilojoule
conversion_factor <- 4.184
# define grouping column
grouping_column <- "Label_group"
# get other labelling columns
other_labelling_columns <- c("Label", "Site", "Cohort", "Date")
# set the predictor of the established model
age_predictor <- "Age"
sex_predictor <- "Sex"
weight_predictor <- "Weight"
height_predictor <- "Height"
basic_predictors <- c(age_predictor, sex_predictor, weight_predictor, height_predictor, "FM", "FFM")
# define microbial predictors (family level)
microbiome_predictors <- column_groups[group == 'microbiome family', column]
# # other microbial columns
# other_microbial_columns <- setdiff(taxa_names, microbial_predictors)
temperature_predictor <- "Mean Outdoor Temperature"
# define the general predictors
general_predictors <- setdiff(names(enable_data), c(response_variable, grouping_column, other_labelling_columns, taxa_names))
# make sure all predictors are in the data
stopifnot(all(c(response_variable, grouping_column, other_labelling_columns, taxa_names, basic_predictors, microbiome_predictors, general_predictors) %in% names(enable_data)))

Load Kiel Data

kiel_data <- data.table::setDT(read_xlsx(file.path(data_folder, "REE Datenbank TUM_Januar 2025tf QM.xlsx")))

## New names:
## • `` -> `...12`
## • `?` -> `?...14`
## • `?` -> `?...15`
## • `?` -> `?...16`
## • `?` -> `?...17`

# make new SampleID from ID and zusätzliche Codierung
kiel_data[, Site := "Kiel"]
kiel_data[, Label := paste0(ID, "_", `zusätzliche Codierung`)]
kiel_data[, Sex := factor(ifelse(`Geschlecht` == 1, "männlich", "weiblich"), levels = levels(enable_data$Sex))]
kiel_data[, Age := Alter]
kiel_data[, Height := `Größe (m)` * 100]
kiel_data[, FM := FM_ADP_kg]
kiel_data[, Weight := `Gewicht (kg)`]
kiel_data[, FFM := Weight - FM]
kiel_data[, Date := `Datum`]
kiel_data[, `Mean Outdoor Temperature` := `daily mean T`]
kiel_data[, RMR := `REE (kcal)` * conversion_factor]

kiel_predictors <- setdiff(intersect(names(enable_data), names(kiel_data)), 
                             other_labelling_columns)
# remove response from kiel predictors
kiel_predictors <- setdiff(kiel_predictors, response_variable)

kiel_data[, (names(enable_data)[!names(enable_data) %in% names(kiel_data)]) := NA]
kiel_only <- setdiff(names(kiel_data), names(enable_data))
kiel_data[, (kiel_only) := NULL]
kiel_data <- kiel_data[, names(enable_data), with=FALSE]

all_data <- rbind(enable_data, kiel_data, use.names=TRUE)
all_data[, Site:=factor(Site, levels = c('Freising', 'Nuremberg', 'Kiel'))]

Build Models

Split and Check Data

suppressPackageStartupMessages(library(tidymodels))
tidymodels_prefer()

# number of NA responses
message(paste("Number of NAs in response: ", all_data |> filter(is.na(get(response_variable))) |> nrow()))

## Number of NAs in response:  8

all_data <- all_data |> subset(!is.na(get(response_variable)))

data.table::transpose(all_data[, c(n = .N, lapply(.SD, function(x) paste(round(mean(x, na.rm=TRUE), 2), round(sd(x, na.rm=TRUE), 2), sep = " ± "))), by=Site, .SDcols = c(age_predictor, "FM", "FFM", response_variable)], keep.names = 'Column', make.names = 'Site')

##    Column          Freising         Nuremberg              Kiel
##    <char>            <char>            <char>            <char>
## 1:      N               351               103               361
## 2:    Age      48.2 ± 18.91      78.28 ± 2.86     43.18 ± 15.19
## 3:     FM     23.21 ± 10.15      28.48 ± 7.78      32.4 ± 14.85
## 4:    FFM     53.82 ± 11.45     47.05 ± 10.63     52.38 ± 13.36
## 5:    RMR 6868.22 ± 1218.15 6399.38 ± 1198.19 6886.54 ± 1308.15

# set seed for reproducibility
set.seed(1)
# split the data by Site to have a test sets
enable_split <- group_initial_split(all_data[Site %in% c('Freising', 'Nuremberg')], group = "Site")
train_data <- enable_split |> training()
test_data <- enable_split |> testing()

# ensure that Site == "freising" in the whole train_data and nuremberg_data 
stopifnot(all(train_data$Site == 'Freising'))
stopifnot(all(test_data$Site == 'Nuremberg'))

# Number of samples that have at least one NA value
message(paste("Number of NAs in any variable: ", train_data |>
  filter_all(any_vars(is.na(.))) |>
  nrow()))

## Number of NAs in any variable:  42

# set number of folds and repeats
nfolds <- 5
nrepeats <- 10

set.seed(1102)
repeated_cv_split <- rsample::vfold_cv(train_data, v = nfolds, repeats = nrepeats)

Configure Recipes

# create recipes
general_recipe <-
  recipe(train_data) |>
  update_role(all_of(taxa_names), new_role = "microbiome") |>
  update_role(all_of(grouping_column), new_role = "splitting indicator") |>
  update_role(all_of(other_labelling_columns), new_role = "labels") |>
  update_role(all_of(response_variable), new_role = "outcome") |>
  update_role(all_of(microbiome_predictors), new_role = "predictor") |>
  update_role(all_of(general_predictors), new_role = "predictor") |>
  step_log(all_of(microbiome_predictors), offset = 1) |>
  step_impute_mean(all_numeric_predictors()) |>
  step_zv(all_predictors()) |>
  step_dummy(all_nominal_predictors()) 

normalized_recipe <- general_recipe |>
  step_normalize(all_numeric_predictors())

accessible_predictors <- kiel_predictors[kiel_predictors != temperature_predictor]

general_accessible_pred_recipe <- general_recipe |>
  update_role(all_of(general_predictors), new_role = "old_predictor") |>
  update_role(all_of(microbiome_predictors), new_role = "old_predictor") |>
  update_role(all_of(accessible_predictors), new_role = "predictor")

normalized_accessible_pred_recipe <- general_accessible_pred_recipe |>
  step_normalize(all_numeric_predictors())
  
# recipe list
recipe_list <- list(general = general_recipe,
                    normalized = normalized_recipe,
                    generalAccessPred = general_accessible_pred_recipe,
                    normalizedAccessPred = normalized_accessible_pred_recipe)

Configure Models

my_metrics <- metric_set(rmse, ccc, rsq, rsq_trad, mae)
main_metric <- names(attr(my_metrics, "metrics"))[1]

# linear model
lm_model <- 
  linear_reg() |> 
  set_engine("lm")

# lasso model
lasso_model <- 
  linear_reg(penalty = tune(), mixture = 1) |> 
  set_engine("glmnet", standardize = TRUE)

# random forest
rf_model <-
  rand_forest(trees = tune(), min_n = tune(), mtry = tune()) |> 
  set_engine("ranger", importance = 'permutation') |> 
  set_mode("regression")

# neural network
nnet_model <- 
   mlp(hidden_units = tune(), penalty = tune(), epochs = tune()) |> 
   set_engine("nnet", MaxNWts = 2600) |> 
   set_mode("regression")

# model list
model_list <- list(linear = lm_model,
                   lasso = lasso_model,
                   RF = rf_model,
                   nnet = nnet_model)

# set the same parameters for all penalties
penalty_range <- penalty(range=c(-10, 3))

# set the parameters for the lasso
lasso_params <-
  lasso_model |>
  extract_parameter_set_dials() |>
  update(penalty = penalty_range)

# set the parameters for the RF
rf_params <-
  rf_model |>
  extract_parameter_set_dials() 

# set the parameters for the NN
nnet_params <- 
   nnet_model |> 
   extract_parameter_set_dials() |> 
   update(hidden_units = hidden_units(c(1, 27))) |>
   update(penalty = penalty_range)

params_list <- list(lasso = lasso_params,
                    RF = rf_params,
                    nnet = nnet_params)

Configure Workflows

grid_size <- 100
# set the workflows
workflows <- workflow_set(
      preproc = c(rep(recipe_list['general'], 3),
                  rep(recipe_list['normalized'], 1),
                  rep(recipe_list['generalAccessPred'], 3),
                  rep(recipe_list['normalizedAccessPred'], 1)),
      models = rep(model_list, 2),
      cross = FALSE)
 
# iterate over the wflow_ids, add paramters and generate the mtry parameter dynamically
for (this_wflow_id in workflows$wflow_id){
  model_name <- data.table::tstrsplit(this_wflow_id, '_', fixed = TRUE, keep = 2)[[1]]
  # set the parameters for the RF in question
  params <- params_list[[model_name]]
  if (model_name == "RF"){
    params <- params |> 
    update(mtry = mtry(c(
      1, sum(recipe_list[[sub("_.*", "", this_wflow_id)]]$var_info$role == "predictor")
    ))) 
  }
  workflows <- workflows |> 
    option_add(param_info = params, id = this_wflow_id)
}

Train Models

require(doMC)

## Loading required package: doMC

## Loading required package: foreach

## 
## Attaching package: 'foreach'

## The following objects are masked from 'package:purrr':
## 
##     accumulate, when

## Loading required package: iterators

## Loading required package: parallel

doMC::registerDoMC(cores = min(nrepeats*nfolds, parallel::detectCores() - 2))

repeated_cv_result_file <- "repeated_cv_results.rds"
if (file.exists(repeated_cv_result_file)) {
  print("loading grid results")
  repeated_cv_result <- readRDS(repeated_cv_result_file)
} else {
  print("creating grid results")
  repeated_cv_result <- workflows |>
    workflow_map(
      fn = "tune_grid",
      seed = 1503,
      resamples = repeated_cv_split,
      grid = grid_size,
      verbose = TRUE,
      metrics = my_metrics,
      control = control_grid(
        save_pred = TRUE
      )
    )
  saveRDS(repeated_cv_result, repeated_cv_result_file)
}

## [1] "loading grid results"

Evaluate Models and Select Best

library(ggpubr)
library(ggplot2)
ggplot2::theme_set(ggplot2::theme_bw() + theme(strip.background = element_rect(fill = "white")))
fig_dir <- "figures"
if(!dir.exists(fig_dir)) dir.create(fig_dir, recursive = TRUE)

autoplot(repeated_cv_result, type="wflow_id")

wflow_ids <- repeated_cv_result$wflow_id
wflow_ids_wo_linear <- wflow_ids[!endsWith(wflow_ids, "_linear")]

final_models <- sapply(wflow_ids_wo_linear, function(this_wflow_id) {
  wflow_results <- repeated_cv_result |> 
    extract_workflow_set_result(this_wflow_id)
  # print(autoplot(wflow_results) + labs(title = this_wflow_id))
  specs <- workflows |> extract_spec_parsnip(this_wflow_id)
  tuning_params <- specs |> extract_parameter_set_dials() |> pull(name)
  if (inherits(specs, "linear_reg")) {
    if (all(c("penalty", "mixture") %in% tuning_params))
      best_model <- wflow_results |> select_by_one_std_err(metric = main_metric, desc(penalty), mixture)
    else if ("penalty" %in% tuning_params) # Lasso
      best_model <- wflow_results |> select_by_one_std_err(metric = main_metric, desc(penalty))
    else if ("mixture" %in% tuning_params)
      best_model <- wflow_results |> select_by_one_std_err(metric = main_metric, mixture)
  } else if (inherits(specs, "rand_forest")) {
    best_model <- wflow_results |> select_by_one_std_err(metric = main_metric, trees, mtry, desc(min_n))
  } else if (inherits(specs, "mlp")) {
    best_model <- wflow_results |> select_by_one_std_err(metric = main_metric, epochs, hidden_units, desc(penalty))
  } else {
    stop("Unknown model")
  }
  best_model
  
}, simplify = FALSE)

one_std_err_results <-
  data.table::rbindlist(
    final_models,
    idcol = 'wflow_id',
    fill = TRUE
  ) |>
  select(wflow_id, .config)
best_results <- repeated_cv_result |> 
  rank_results(rank_metric = main_metric, select_best = TRUE) |>
  select(wflow_id, .config) |>
  unique()
results_to_keep <- rbind(one_std_err_results, best_results)

repeated_cv_result_dt <- repeated_cv_result |> rank_results(rank_metric = main_metric) |> semi_join(results_to_keep)
repeated_cv_result_dt[, rank := factor(rank, levels = sort(unique(rank)))]

ggplot(repeated_cv_result_dt, aes(x = rank, y = mean, color = wflow_id)) +
  geom_point() +
  geom_errorbar(aes(ymin = mean - std_err, ymax = mean + std_err), width = .5) +
  facet_wrap(~.metric, scales = 'free')

final_fits <- sapply(names(final_models), function(this_wflow_id)
  repeated_cv_result |>
         extract_workflow(this_wflow_id) |>
         finalize_workflow(final_models[[this_wflow_id]]) |>
         last_fit(split = enable_split, metrics=my_metrics),
  simplify = FALSE)

linear_models <- sapply(wflow_ids[!wflow_ids %in% wflow_ids_wo_linear], function(this_wflow_id){
  this_recipe_name <- sub(pattern = '_.*$', replacement = '', this_wflow_id)
  workflow() |> 
    add_recipe(recipe_list[[this_recipe_name]]) |>
    add_model(lm_model) |> 
    last_fit(split = enable_split, metrics = my_metrics)
}, simplify = FALSE)
fits <- c(final_fits, linear_models)
repeated_cv_result_dt <- repeated_cv_result_dt |> semi_join(one_std_err_results |> rbind(best_results |> subset(endsWith(wflow_id, "linear"))))
main_model <- repeated_cv_result_dt[.metric == main_metric][which.min(mean), wflow_id]

Evaluate Lasso Feature Robustness

library(glmnet)

feature_colors <- c(
  "FFM" = "#009999",          # Teal (greenish for FFM_SECA)
  "Weight" = "#B2DF8A",    # Light Green (for GEWICHt_SECA)
  "Mean Outdoor Temperature" = "#000000",           # Black (for mean_temp)
  "GFR" = "#ff6db6",     # Pink (blood measure GFRCKDE)
  "fT3" = "#b66dff",          # Purple (blood measure fT3)
  "MCHC" = "#490092",          # Dark Purple (blood measure MCHC)
  "Unexplained" = "#db6d00",         # Orange (for Unexplained)
  "Intra-Individual Variation" = "#FDB462" # Light Orange (for Individual Variation)
)

stability_dt <- data.table::rbindlist(sapply(recipe_list[c("general", "generalAccessPred")], 
                                             FUN = function(this_recipe){
  # prepare x and y data
  prepped_training_data <- this_recipe |> step_select(c(all_predictors(), all_outcomes())) |> prep() |> bake(NULL)
  x <- prepped_training_data |> select(-any_of(response_variable)) |> as.matrix()
  y <- prepped_training_data |> pull(response_variable)
  
  # get the repeats from our repeated split
  repeat_ids <- repeated_cv_split$id |> unique()
  
  # lasso runs per repeat
  cvfits <- 
    lapply(repeat_ids, function(repeat_id) {
    # Filter the splits for the specified repeat
    repeat_splits <- repeated_cv_split |> subset(id == repeat_id)
    
    # Initialize a fold ID vector (length = number of rows in the data)
    fold_ids <- integer(prepped_training_data |> nrow())
    
    # Assign fold numbers to each observation based on assessment sets
    for (i in seq_along(repeat_splits$splits)) {
      fold <- repeat_splits$splits[[i]]
      assessment_indices <- tidy(fold) |> subset(Data == "Assessment") |> pull(Row)
      fold_ids[assessment_indices] <- i  # Assign fold number `i` to assessment indices
    }
    stopifnot(all(fold_ids>0))
    
    lasso <-
      cv.glmnet(
        x = x,
        y = y,
        alpha = 1,
        family = "gaussian",
        foldid = fold_ids,
        standardize = TRUE
      )
    
    lasso
  }) 
  names(cvfits) <- repeat_ids
  
  nonzero_coefs <- lapply(cvfits, function(cvfit) {
    # get the nonzero coefficients
    coefs <- coef(cvfit, s = "lambda.1se")
    nonzero_coefs <- coefs[coefs[, 1] != 0, ]
    sort(nonzero_coefs, decreasing = TRUE)
    names(nonzero_coefs)
    })
  names(nonzero_coefs) <- repeat_ids
  
  transposed_df <- stack(nonzero_coefs)
  # remove intercept from values
  transposed_df <- data.table::setDT(transposed_df) |> subset(values != "(Intercept)")
  transposed_df
}, simplify = FALSE), idcol = 'recipe')

stability_dt[recipe == "general", Features := "Enable Features"]
stability_dt[recipe == "generalAccessPred", Features := "Accessible Features"]
stability_dt[, Features := factor(Features, levels = c("Enable Features", "Accessible Features"))]

ggplot(stability_dt, aes(x = reorder(values, ind, function(x) -length(x)), fill = values)) +
    geom_bar() +
    scale_fill_manual(values = feature_colors) +
    facet_grid(Features ~.) +
    theme(axis.text.x = element_text(angle = 45, hjust = 1), legend.position = 'none') +
    labs(title = "Lasso Feature Robustness", x = "Feature", y = "Number of Times Selected")

ggsave(file.path(fig_dir, "lasso_feature_robustness_both.pdf"), width = 6, height = 5)

Evaluate Best Lasso Coefficients

# Function to calculate luminance
calculate_luminance <- function(hex_color) {
  rgb <- col2rgb(hex_color) / 255
  # Apply relative luminance formula
  luminance <- 0.2126 * rgb[1, ] + 0.7152 * rgb[2, ] + 0.0722 * rgb[3, ]
  return(luminance)
}

# Decide text color (black or white) based on luminance threshold
text_colors <- sapply(feature_colors, function(color) {
  if (calculate_luminance(color) > 0.5) {
    "black"  # Light background -> Black text
  } else {
    "white"  # Dark background -> White text
  }
})
selected_coefs <- sapply(names(fits)[endsWith(names(fits), 'lasso')], function(wflow_id){
  selected_coefs <- fits[[wflow_id]] |> 
    extract_fit_parsnip() |> tidy() |> subset(estimate != 0) |> 
    mutate(abs_estimate = abs(estimate)) |> arrange(desc(abs_estimate)) |> select(-abs_estimate)
}, simplify = FALSE)
print(sub(pattern = "x (Intercept) ", replacement = "", x = selected_coefs$general_lasso[, paste(round(estimate, 1), term, sep = " x ", collapse = " + ")], fixed = TRUE))

## [1] "1520.2 + 92.3 x fT3 + 67.5 x FFM + 17.2 x MCHC + -14 x Mean Outdoor Temperature + 9.7 x Weight + 2.4 x GFR"

print(sub(pattern = "x (Intercept) ", replacement = "", x = selected_coefs$generalAccessPred_lasso[, paste(round(estimate, 1), term, sep = " x ", collapse = " + ")], fixed = TRUE))

## [1] "2369.6 + 69.2 x FFM + 13.8 x Weight + -6 x Age"

selected_coefs

## $general_lasso
## # A tidytable: 7 × 3
##   term                     estimate penalty
##   <chr>                       <dbl>   <dbl>
## 1 (Intercept)               1520.      129.
## 2 fT3                         92.3     129.
## 3 FFM                         67.5     129.
## 4 MCHC                        17.2     129.
## 5 Mean Outdoor Temperature   -14.0     129.
## 6 Weight                       9.70    129.
## 7 GFR                          2.36    129.
## 
## $generalAccessPred_lasso
## # A tidytable: 4 × 3
##   term        estimate penalty
##   <chr>          <dbl>   <dbl>
## 1 (Intercept)  2370.      60.5
## 2 FFM            69.2     60.5
## 3 Weight         13.8     60.5
## 4 Age            -6.03    60.5

Build More Complex Linear Models

selected_features <- selected_coefs$general_lasso |> subset(term != '(Intercept)') |> pull(term)
inaccessible_features <- selected_features[!selected_features %in% accessible_predictors]

# now let's make another recipe using only those features
selected_recipe <- general_recipe |>
  update_role(all_of(general_predictors), new_role = "old_predictor") |>
  update_role(all_of(microbiome_predictors), new_role = "old_predictor") |>
  update_role(all_of(selected_features), new_role = "predictor")

quadratic_recipe <- selected_recipe |>
  step_poly(all_numeric_predictors(), degree = 2) 

interaction_recipe <- selected_recipe |>
  step_interact(~ all_predictors():all_predictors())

selectedAccessible_recipe <- selected_recipe |>
  update_role(all_of(inaccessible_features), new_role = "old_predictor")

selectedWTempAccessible_recipe <- selectedAccessible_recipe |>
  update_role(all_of(temperature_predictor), new_role = "predictor")

new_recipes <- list(selected = selected_recipe, 
                    quadratic = quadratic_recipe, 
                    interaction = interaction_recipe,
                    selectedAccess = selectedAccessible_recipe,
                    selectedWTempAccess = selectedWTempAccessible_recipe
                    )

new_recipe_repeated_cv_results <- workflow_set(
      preproc = new_recipes,
      models = list(linear = lm_model)) |>
      workflow_map(
        fn = "fit_resamples",
        seed = 1503,
        resamples = repeated_cv_split,
        verbose = TRUE,
        metrics = my_metrics
      ) |> rank_results()

## i 1 of 5 resampling: selected_linear

## ✔ 1 of 5 resampling: selected_linear (1.4s)

## i 2 of 5 resampling: quadratic_linear

## ✔ 2 of 5 resampling: quadratic_linear (1.5s)

## i 3 of 5 resampling: interaction_linear

## ✔ 3 of 5 resampling: interaction_linear (1.4s)

## i 4 of 5 resampling: selectedAccess_linear

## ✔ 4 of 5 resampling: selectedAccess_linear (1.4s)

## i 5 of 5 resampling: selectedWTempAccess_linear

## ✔ 5 of 5 resampling: selectedWTempAccess_linear (1.5s)

# ggplot(new_recipe_repeated_cv_results, aes(x = rank, y = mean, color = wflow_id)) +
#     geom_point() +
#     geom_errorbar(aes(ymin = mean - std_err, ymax = mean + std_err), width = .5) +
#     facet_wrap(~.metric, scales = 'free')

repeated_cv_result_dt <- rbind(repeated_cv_result_dt, new_recipe_repeated_cv_results)
# rerank the results based on the main metric
repeated_cv_result_dt[, wflow_id2 := factor(wflow_id, levels = repeated_cv_result_dt[.metric == main_metric][order(mean), wflow_id])]
# ggplot(repeated_cv_result_dt, aes(x = wflow_id2, y = mean, color = model)) +
#     geom_point() +
#     geom_errorbar(aes(ymin = mean - std_err, ymax = mean + std_err), width = .5) +
#     facet_wrap(~.metric, scales = 'free') +
#   # rotate x-axis labels 90 degree
#   theme(axis.text.x = element_text(angle = 45, hjust = 1))

recipe_list <- c(recipe_list, new_recipes)

new_models <- sapply(new_recipes, 
       function(this_recipe){
         workflow() |> 
           add_recipe(this_recipe) |>
           add_model(lm_model) |>
           last_fit(split = enable_split, metrics = my_metrics)
}, simplify = FALSE)
names(new_models) <- paste(names(new_models), 'linear', sep = "_")
fits <- c(fits, new_models)

Current Methods in Literature

established_models <- c(`Harris-Benedict` = 'Harris-Benedict', WHO = 'WHO', `Kleiber` = 'Kleiber')

HarrisBenedict <- function(weight, height, age, sex_female){
  ifelse(sex_female, 
         655.1 + 9.6*weight + 1.8*height - 4.7*age,
         66.47 + 13.7*weight + 5*height - 6.8*age) * conversion_factor
}

Kleiber <- function(weight){
  283 * weight^0.75
}

WHO <- function(weight, age, sex_female) {
  
  # Initialize RMR vector
  RMR <- numeric(length(weight))
  
  # Define reusable age filters
  age_filter <- list(
    age_3_10 = age <= 10,
    age_10_30 = age >= 18 & age <= 30,
    age_30_60 = age > 30 & age <= 60,
    age_60_plus = age > 60
  )
  
  # Calculate RMR for each age group using `ifelse` conditioned on `sex_female`
  RMR[age_filter$age_3_10] <- ifelse(sex_female[age_filter$age_3_10],
                                     (22.5 * weight[age_filter$age_3_10] + 499),
                                     (22.7 * weight[age_filter$age_3_10] + 495))
  
  RMR[age_filter$age_10_30] <- ifelse(sex_female[age_filter$age_10_30],
                                      (14.7 * weight[age_filter$age_10_30] + 496),
                                      (15.3 * weight[age_filter$age_10_30] + 679))
  
  RMR[age_filter$age_30_60] <- ifelse(sex_female[age_filter$age_30_60],
                                      (8.7 * weight[age_filter$age_30_60] + 829),
                                      (11.6 * weight[age_filter$age_30_60] + 879))
  
  RMR[age_filter$age_60_plus] <- ifelse(sex_female[age_filter$age_60_plus],
                                        (10.5 * weight[age_filter$age_60_plus] + 596),
                                        (13.5 * weight[age_filter$age_60_plus] + 487))
  
  return(RMR*conversion_factor)
}

Visualize Interesting Models

interesting_models <- c(`Lasso Enable` = "general_lasso", 
                        `Lasso Accessible` = "generalAccessPred_lasso",
                        established_models
                        )

# Swap names and values
interesting_modelmap <- setNames(names(interesting_models), interesting_models)

repeated_cv_result_dt[wflow_id %in% interesting_models, wflow_id := interesting_modelmap[wflow_id]]

# get the fits for the interesting models
interesting_fits <- fits[interesting_models]
# remove NULLs
interesting_fits <- interesting_fits[!sapply(interesting_fits, is.null)]

interesting_model_estimates <- data.table::rbindlist(lapply(interesting_fits, function(fit) fit |> extract_fit_parsnip() |> tidy() |> subset(estimate != 0) |> mutate(abs_estimate = abs(estimate)) |> arrange(desc(abs_estimate)) |> select(-abs_estimate)), idcol = 'model', fill = TRUE)

interesting_model_estimates[, model := interesting_modelmap[model]]
interesting_model_estimates[, term := gsub(pattern = '`', replacement = '', x = term, fixed = TRUE)]

print(interesting_model_estimates[term != '(Intercept)', paste(.SD[order(-abs(estimate)), term], collapse = "; "), by = model])

##               model                                                    V1
##              <char>                                                <char>
## 1:     Lasso Enable fT3; FFM; MCHC; Mean Outdoor Temperature; Weight; GFR
## 2: Lasso Accessible                                      FFM; Weight; Age

Compute Predictions and Metrics

interesting_metrics <- c(RMSE = 'rmse', R2 = 'rsq_trad')
rounding_by <- c(
  RMSE = 0,
  R2 = 3
)
interesting_metricmap <- setNames(names(interesting_metrics), interesting_metrics)


predict_data_fits <- function(fits, recipe_list, truth, new_data = NULL) {
  data.table::rbindlist(
    sapply(names(fits), function(this_wflow_id) {
      last_fit <- fits[[this_wflow_id]]
      this_recipe_name <- sub(pattern = '_.*$', replacement = '', this_wflow_id)
      this_recipe <- recipe_list[[this_recipe_name]]
      prepped_data <- this_recipe |> step_select(all_of(c(all_predictors(), all_outcomes()))) |> prep() |> bake(new_data = new_data)
      last_fit |> extract_fit_parsnip() |> predict(new_data = prepped_data) |> mutate(truth = truth)
    }, simplify = FALSE),
    idcol = 'model'
  ) |> rename(estimate = .pred)
}

predict_data_established <- function(new_data, truth){
  data.table::rbindlist(list(
    data.table::data.table(model = established_models['Harris-Benedict'], 
                           estimate = HarrisBenedict(weight = new_data[[weight_predictor]],
                                                     height = new_data[[height_predictor]],
                                                     age = new_data[[age_predictor]],
                                                     new_data[[sex_predictor]] == 'weiblich'),
                           truth = truth),
    data.table::data.table(model = established_models['Kleiber'], 
                           estimate = Kleiber(weight = new_data[[weight_predictor]]),
                           truth = truth),
    data.table::data.table(model = established_models['WHO'], 
                           estimate = WHO(weight = new_data[[weight_predictor]], 
                                          age = new_data[[age_predictor]],
                                          sex_female = new_data[[sex_predictor]] == 'weiblich'),
                           truth = truth)
    )
  )
}

compute_my_metrics <- function(preds, my_metrics, metrics_to_keep, n_bootstrap_samples = 10000, seed = 4735684){
  metric_dt <- preds[, my_metrics(.SD, truth = truth, estimate = estimate), by=model]
  if (n_bootstrap_samples > 0) {
    set.seed(seed)
    # # data.table only solution is too slow
    # # Get sizes per model
    # model_sizes <- preds[ , .N, by = model]
    # # Create bootstrap sample indices
    # boot_dt <- model_sizes[ , .(
    #   bootstrap_ind = rep(1:n_bootstrap_samples, each = N),
    #   row_id = sample(seq.int(N), size = N * n_bootstrap_samples, replace = TRUE)
    # ), by = model]
    # # Now compute metrics per bootstrap sample
    # bootstrap_metrics <- boot_dt[preds, on = .(model, row_id)][ , my_metrics(.SD, truth = truth, estimate = estimate), by = .(bootstrap_ind, model)]
    
    bootstrap_indices <- replicate(n_bootstrap_samples, sample(preds[ , .N, by = model][, unique(N)], replace = TRUE), simplify = FALSE)
    bootstrap_metrics <- data.table::rbindlist(pbmcapply::pbmclapply(bootstrap_indices, function(indices) {
      preds[ , my_metrics(.SD[indices], truth = truth, estimate = estimate), by=model]
    }, mc.cores = min(n_bootstrap_samples/10, parallel::detectCores() / 2)), idcol = 'bootstrap_ind')
    metric_dt <- rbind(metric_dt, bootstrap_metrics, use.names = TRUE, fill = TRUE)
    # metric_int <- bootstrap_metrics[, .(lower = quantile(.estimate, 0 + ((1 - .9)/2)), mean = mean(.estimate), higher = quantile(.estimate, 1 - ((1 - .9)/2))), by = .(model, .metric)]
    # metric_dt[metric_int, on = .NATURAL, c("lower", "mean", "higher") := .(lower, mean, higher)]
  }
  # metric_dt <- data.table::dcast(metric_dt, model ~ .metric, value.var = '.estimate')
  # data.table::setnames(metric_dt, old = metrics_to_keep, new = names(metrics_to_keep))
  # metric_dt[, metrics_string := do.call(
  #     paste,
  #     c(Map(function(name, value) paste(name, round(value, rounding_by[name]), sep = ": "), names(metrics_to_keep), mget(names(metrics_to_keep))), sep = "\n ")
  # )]
  metric_dt
}

data_by_site <- split(all_data, all_data$Site)
data_by_site$KielWoTemp <- data.table::copy(data_by_site$Kiel)
data_by_site$KielWoTemp[, (temperature_predictor) := NA]

bmi_dt <- all_data[, .(Site, response_check=get(response_variable), BMI = Weight/((Height/100)^2))]

preds_by_site <- sapply(names(data_by_site), function(this_data_name){
  this_data <- data_by_site[[this_data_name]]
  
  fit_preds <- predict_data_fits(fits = fits, 
                                 recipe_list = recipe_list, 
                                 truth = this_data[[response_variable]], 
                                 new_data = this_data)
  fit_preds <- rbind(
    fit_preds,
    predict_data_established(new_data = this_data, truth = this_data[[response_variable]])
  )
  # match the bmi to the predictions
  bmi_site <- bmi_dt[, unique(Site)[sapply(as.character(unique(Site)), function(site) startsWith(this_data_name, site))]]
  fit_preds[, c("BMI", "response_check") := bmi_dt[Site == bmi_site, .(BMI, response_check)], by = 'model']
  stopifnot(fit_preds[, identical(truth, response_check)])
  fit_preds[, response_check := NULL]
  
  fit_preds
}, simplify = FALSE)

metrics_by_site <- lapply(preds_by_site, compute_my_metrics, my_metrics = my_metrics, metrics_to_keep = interesting_metrics)

pred_dt <- data.table::rbindlist(preds_by_site, idcol = 'Site')
metric_dt <- data.table::rbindlist(metrics_by_site, idcol = 'Site')

metric_dt[.metric %in% interesting_metrics, .metric := interesting_metricmap[.metric]]

pred_dt[, Site := factor(Site, levels = c(all_data[, levels(Site)], "KielWoTemp"))]
metric_dt[, Site := factor(Site, levels = c(all_data[, levels(Site)], "KielWoTemp"))]

pred_dt[model %in% interesting_models, model := interesting_modelmap[model]]
metric_dt[model %in% interesting_models, model := interesting_modelmap[model]]

# sort pred_dt and metric_dt 
pred_dt[, model := factor(model, levels = c(interesting_modelmap, unique(model[!model %in% interesting_modelmap])))]
metric_dt[, model := factor(model, levels = c(interesting_modelmap, unique(model[!model %in% interesting_modelmap])))]


pred_dt[grep("lasso", model, ignore.case = TRUE), `Model Type` := "Lasso"]
pred_dt[model %in% established_models, `Model Type` := "Established"]

Plots

Summary

CV Summary

model_type_colors <- c(Established = "#66C2A5",
                       Lasso = "#FC8D62",
                       Nnet = "#8DA0CB", 
                       RF = "#E78AC3",
                       Linear = "#A6D854")

repeated_cv_result_dt[, c("prepping", "Model Type") := data.table::tstrsplit(as.character(wflow_id2), "_", fixed = TRUE)]
repeated_cv_result_dt[, `Model Type` := tools::toTitleCase(`Model Type`)]
repeated_cv_result_dt[, `Accessible Predictors` := grepl(pattern = "Access", x = prepping)]

ggplot(repeated_cv_result_dt[!wflow_id2 %in% names(new_models) & .metric == main_metric], aes(x = reorder(wflow_id, mean), y = mean, color = `Model Type`, shape = `Accessible Predictors`)) +
    geom_point(size = 3) +
    geom_errorbar(aes(ymin = mean - std_err, ymax = mean + std_err), width = .5) +
    scale_shape_manual(values = c(5, 16)) +
    scale_color_manual(values = model_type_colors) +
    theme(axis.text.x = element_blank(), axis.ticks.x = element_blank(),
          legend.position = c(.01, .99),
          legend.justification = c("left", "top"),
          legend.box.background = element_rect(linewidth = .1),
          legend.background = element_rect(fill = NA))+
    labs(x = NULL, y = interesting_metricmap[main_metric], title = "Cross-Validation Summary")

## Warning: A numeric `legend.position` argument in `theme()` was deprecated in ggplot2
## 3.5.0.
## ℹ Please use the `legend.position.inside` argument of `theme()` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

ggsave(filename = file.path(fig_dir, "cv_summary.pdf"), width = 5, height = 4)

Test Summary

require(tidytext)

## Loading required package: tidytext

summary_metrics <- data.table::copy(metric_dt)
summary_metrics[Site == "KielWoTemp", Site := "Kiel Without Temperature"]
data.table::setnames(summary_metrics, c(".metric", ".estimate"), c("metric_name", "metric"))
summary_metrics[grep("linear", model, ignore.case = TRUE), `Model Type` := "Linear"]
summary_metrics[grep("lasso", model, ignore.case = TRUE), `Model Type` := "Lasso"]
summary_metrics[model %in% established_models, `Model Type` := "Established"]

wide_bootstrap_res <- data.table::dcast(summary_metrics, formula = Site + metric_name + bootstrap_ind ~ model, value.var = "metric")
pairwise_comparisons <- data.table::CJ(model1 = ordered(interesting_modelmap, levels = interesting_modelmap), 
                                       model2 = ordered(interesting_modelmap, levels = interesting_modelmap))[model1 < model2]
pairwise_tests <- wide_bootstrap_res[, 
                                     .(list = lapply(1:nrow(pairwise_comparisons), function(i){
                                       m1 <- as.character(pairwise_comparisons[i, model1])
                                       m2 <- as.character(pairwise_comparisons[i, model2])
                                       delta <- get(m1) - get(m2)
                                      
                                      # Observed difference
                                      delta_obs <- delta[is.na(bootstrap_ind)]
                                      
                                      # Bootstrap differences centered at their bootstrap mean
                                      delta_star <- delta[!is.na(bootstrap_ind)]
                                      delta_star_centered <- delta_star - mean(delta_star)
                                      
                                      # p-value: proportion of bootstrap differences >= observed difference
                                      p_value <- mean(abs(delta_star_centered) >= abs(delta_obs))
                                      
                                       .(.y. = 'metric', 
                                         p = p_value, 
                                         mean_delta = mean(delta), 
                                         group1 = m1, 
                                         group2 = m2)
                                     })), by = .(Site, metric_name)][, data.table::rbindlist(list), by = .(Site, metric_name)]


# interesting_comparisons <- data.table(group1 = interesting_modelmap[-length(interesting_modelmap)], group2 = interesting_modelmap[-1])

pairwise_tests[, group1 := paste(group1, Site, sep = "___")]
pairwise_tests[, group2 := paste(group2, Site, sep = "___")]

pairwise_tests_summary <- pairwise_tests[metric_name %in% interesting_metricmap &
                                           Site %in% c("Freising", "Nuremberg", "Kiel")]
pairwise_tests_summary[, p.adj :=  p.adjust(p, method = "BH"), by = .(Site, metric_name)]
pairwise_tests_summary[, p.signif := as.character(stats::symnum(x = p.adj, 
                                       cutpoints = c(0, 1e-04, 0.001, 0.01, 0.05, 1), 
                                       symbols = c("****", "***", "**", "*", "ns")))]

score_summary_metrics <- summary_metrics[model %in% interesting_modelmap &
                                        metric_name %in% interesting_metricmap &
                                        Site %in% c("Freising", "Nuremberg", "Kiel")]

pairwise_tests_summary[score_summary_metrics[!is.na(bootstrap_ind), 
                                     .(y.position = max(metric)), 
                                     by = .(Site, metric_name)],
               on = .NATURAL,
               y.position := y.position]
pairwise_tests_summary[, y.position := y.position + y.position * (.05 * (seq.int(.N) - 1)), by = .(Site, metric_name)]
pairwise_tests_summary[metric_name == "RMSE", y.position := y.position - 200]


score_summary <- ggplot(score_summary_metrics[!is.na(bootstrap_ind)],
       aes(x = tidytext::reorder_within(model, metric, Site), y = metric)) +
    geom_col(data = score_summary_metrics[is.na(bootstrap_ind)], aes(fill = `Model Type`), color = 'white', alpha = 0.7) +
    stat_summary(fun.data = function(x) list(y = mean(x), ymin = quantile(x, 0 + ((1 - .9)/2)), ymax = quantile(x, 1 - ((1 - .9)/2))), 
                 geom = "pointrange", fatten = 2) +
    stat_pvalue_manual(pairwise_tests_summary, 
                       label = "p.signif", tip.length = 0, size = 2) +
    scale_fill_manual(values = model_type_colors) +
    coord_cartesian(ylim = c(0, NA)) +
    # add the value as text into the bar, ninety degrees rotated
    geom_text(data = score_summary_metrics[is.na(bootstrap_ind)], aes(label = round(metric, rounding_by[metric_name]), y = 0), hjust = -.15, vjust = 1.4, angle = 90) +
    facet_grid(metric_name ~ Site, scales = "free") +
    labs(x = NULL, y = NULL) +
    tidytext::scale_x_reordered() +
    theme(axis.text.x = element_text(angle = 45, hjust = 1), legend.position = "left")
ggsave(filename = file.path(fig_dir, "score_summary.pdf"), plot = score_summary, width = 8, height = 6)

score_summary_metrics_kiel <- summary_metrics[model %in% interesting_modelmap[!interesting_modelmap %in% established_models] & 
                                                metric_name %in% interesting_metricmap &
                                                Site %in% c("Kiel", "Kiel Without Temperature")]

pairwise_tests_summary_kiel <- 
  pairwise_tests[grepl(pattern = paste(interesting_modelmap[!interesting_modelmap %in% established_models], collapse = "|"), x = group1) &
                 grepl(pattern = paste(interesting_modelmap[!interesting_modelmap %in% established_models], collapse = "|"), x = group2) &
                 metric_name %in% interesting_metricmap &
                Site %in% c("Kiel", "Kiel Without Temperature")]

pairwise_tests_summary_kiel[, p.signif := as.character(stats::symnum(x = p.adjust(p, method = "BH"), 
                                       cutpoints = c(0, 1e-04, 0.001, 0.01, 0.05, 1), 
                                       symbols = c("****", "***", "**", "*", "ns"))), 
                       by = .(Site, metric_name)]



pairwise_tests_summary_kiel[score_summary_metrics_kiel[!is.na(bootstrap_ind), 
                                     .(y.position = max(metric)), 
                                     by = .(Site, metric_name)],
               on = .NATURAL,
               y.position := y.position]
pairwise_tests_summary_kiel[, y.position := y.position + y.position * (.05 * (seq.int(.N) - 1)), by = .(Site, metric_name)]

score_summary_kiel <- ggplot(score_summary_metrics_kiel[!is.na(bootstrap_ind)],
    aes(x = tidytext::reorder_within(model, metric, Site), y = metric)) +
    geom_col(data = score_summary_metrics_kiel[is.na(bootstrap_ind)], aes(fill = `Model Type`), color = 'white', alpha = 0.7) +
    stat_summary(fun.data = function(x) list(y = mean(x), ymin = quantile(x, 0 + ((1 - .9)/2)), ymax = quantile(x, 1 - ((1 - .9)/2))), 
                 geom = "pointrange", fatten = 2) +
    stat_pvalue_manual(pairwise_tests_summary_kiel, label = "p.signif", tip.length = 0, size = 2) +
    scale_fill_manual(values = model_type_colors) +
    # add the value as text into the bar, ninety degrees rotated
    geom_text(data = score_summary_metrics_kiel[is.na(bootstrap_ind)], aes(label = round(metric, rounding_by[metric_name]), y = 0), hjust = -.15, angle = 90) +
    facet_grid(metric_name ~ Site, scales = "free") +
    labs(x = NULL, y = NULL) + 
    tidytext::scale_x_reordered() + 
    theme(axis.text.x = element_text(angle = 45, hjust = 1), legend.position = "none")
ggsave(filename = file.path(fig_dir, "score_summary_kiel.pdf"), plot = score_summary_kiel, width = 4, height = 4)

Prediction and Error Plots

plot_preds <- function(preds, metric_dt, main_metric, facet_col = "Site", facet_row = "model", color_col = "Model Type", focus_observed = FALSE){
  p <- ggplot(preds, aes(x = truth, y = estimate, color = get(color_col))) +
    geom_abline(color = "gray50", lty = 2) + 
    geom_point(alpha = 0.5) + 
    labs(title = NULL, x = 'Observed RMR in kJ/day', y = 'Predicted RMR in kJ/day') +
    theme(legend.position = "none") +
    geom_label(data = metric_dt, aes(x = -Inf, y = Inf, label = metrics_string), 
               vjust = 1.1, hjust = -0.1, inherit.aes = FALSE, size = 3)
  if (preds[, !is.numeric(get(color_col))])
    p <- p + scale_color_manual(values = model_type_colors)
  else 
    p <- p + scale_color_gradient2()
  if (facet_col != "" & facet_row != "") {
    p <- p + facet_grid(get(facet_col) ~ get(facet_row))
  }
  if (focus_observed) {
    p <- p +
      coord_obs_pred(xlim=c(min(preds$truth), max(preds$truth)),
                     ylim=c(min(preds$truth), max(preds$truth)))
  } else {
    p <- p +
      coord_obs_pred()
  }
  p
}

plot_bland_altman <- function(preds, metric_dt, main_metric, facet_col = "Site", facet_row = "model", color_col = "Model Type") {
  preds[, mean_measurement := (truth + estimate) / 2]
  preds[, difference := truth - estimate]
  if (facet_col != "" & facet_row != "") {
    preds[, mean_difference := mean(difference), by=.(get(facet_row), get(facet_col))]
    preds[, lower_difference:= mean_difference - sd(difference)*1.96, by=.(get(facet_row), get(facet_col))]
    preds[, upper_difference:= mean_difference + sd(difference)*1.96, by=.(get(facet_row), get(facet_col))]
  } else {
    preds[, mean_difference := mean(difference)]
    preds[, lower_difference:= mean_difference - sd(difference)*1.96]
    preds[, upper_difference:= mean_difference + sd(difference)*1.96]
  }
  
  p <- ggplot(preds, aes(x = mean_measurement, y = difference, color = get(color_col))) +
    geom_hline(aes(yintercept = mean_difference)) +
    geom_hline(aes(yintercept = lower_difference), linetype = 'dashed') +
    geom_hline(aes(yintercept = upper_difference), linetype = 'dashed') +
    geom_point(alpha = 0.5) + 
    labs(title = NULL, x = 'Mean of Observed and Predicted', y = 'Observed - Predicted') +
    theme(legend.position = "none")
  
  if (preds[, !is.numeric(get(color_col))])
    p <- p + scale_color_manual(values = model_type_colors)
  
  if (facet_col != "" & facet_row != "") {
    p <- p + facet_grid(get(facet_col) ~ get(facet_row))
  }
  p
}

sites <- c("Freising", "Nuremberg", "Kiel", "KielWoTemp")
models <- c(interesting_modelmap[startsWith(interesting_modelmap, "Lasso")],
            established_models)
pred_dt[, `BMI Category` := cut(BMI, breaks = c(0, 16, 17, 18.5, 25, 30, 35, 40, Inf), right = FALSE)]
pred_dt[, `BMI Category` := factor(`BMI Category`, levels = c("[0,16)", "[16,17)", "[17,18.5)", "[18.5,25)", "[25,30)", "[30,35)", "[35,40)", "[40,Inf)"))]
bmi_mapping <- c(`[0,16)` = "Underweight (Severe thinness)",
                 `[16,17)` = "Underweight (Moderate thinness)",
                 `[17,18.5)` = "Underweight (Mild thinness)",
                 `[18.5,25)` = "Normal range",
                 `[25,30)` = "Overweight (Pre-obese)",
                 `[30,35)` = "Obese (Class I)",
                 `[35,40)` = "Obese (Class II)",
                 `[40,Inf)` = "Obese (Class III)")
pred_dt[, `BMI Category` := bmi_mapping[`BMI Category`]]
pred_dt[, `BMI Category` := ordered(`BMI Category`, levels = bmi_mapping)]

bmi_colors <- c("#7c7cbd", "#7c7cfd", "#7cfcfc", "#7cfc7c", "#fcfc7c", "#fcbb91", "#fc9192", "#c08081")
names(bmi_colors) <- bmi_mapping

metric_string_dt <- data.table::dcast(metric_dt[is.na(bootstrap_ind)], model + Site ~ .metric, value.var = '.estimate')[, metrics_string := do.call(
    paste,
    c(Map(function(name, value) paste(name, round(value, rounding_by[name]), sep = ": "), interesting_metricmap, mget(interesting_metricmap)), sep = "\n ")
)]

pred_obs <-
        plot_bland_altman(
          pred_dt[model %in% models &
                    Site %in% sites],
          metric_string_dt[model %in% models &
                           Site %in% sites],
          main_metric = interesting_metricmap[main_metric],
          facet_col = "Site",
          facet_row = "model",
          color_col = "BMI Category"
        )
# print(pred_obs + 
#         geom_point(alpha = 1, size = .5) +
#         guides(color = guide_legend(byrow = T)) +
#         scale_color_manual(values = bmi_colors) +
#         theme(legend.position = "top") + labs(color = "BMI Category"))
print(pred_obs + 
        geom_point(alpha = 1, size = .4) +
        guides(color = guide_legend(byrow = T)) +
        scale_color_brewer(palette = "RdYlBu", direction = -1) +
        theme(legend.position = "top") + labs(color = "BMI Category"))

## Scale for colour is already present.
## Adding another scale for colour, which will replace the existing scale.

# print(pred_obs + 
#         geom_point(alpha = 1, size = .5) +
#         guides(color = guide_legend(byrow = T)) +
#         scale_color_brewer(type = "div", direction = -1) +
#         theme(legend.position = "top") + labs(color = "BMI Category"))

library(patchwork)
pred_plots <-
  mapply(
    sites = list(c("Freising", "Nuremberg", "Kiel", "KielWoTemp"),
                 c("Freising")),
    models = list(
      c(interesting_modelmap[startsWith(interesting_modelmap, "Lasso")],
        established_models
    ), 
      c("Lasso Enable")),
    fig.sizes = list(c(15, 15), 
                     c(4, 4)),
    FUN = function(sites, models, fig.sizes) {
      fig_suffix <- paste0(paste(sites, collapse="-"), "_", paste(models, collapse="-"), ".pdf")
      pred_obs <-
        plot_preds(
          pred_dt[model %in% models &
                    Site %in% sites],
          metric_string_dt[model %in% models &
                           Site %in% sites],
          main_metric = interesting_metricmap[main_metric],
          facet_col = ifelse(length(sites) > 1, "Site", ""),
          facet_row = ifelse(length(models) > 1, "model", ""),
          focus_observed = TRUE
        )
      print(pred_obs)
      ggsave(filename = file.path(fig_dir, paste0("pred_obs_", fig_suffix)), plot = pred_obs, width = fig.sizes[1], height = fig.sizes[2])
      ba <-
        plot_bland_altman(
          pred_dt[model %in% models &
                    Site %in% sites],
          metric_string_dt[model %in% models &
                           Site %in% sites],
          main_metric = interesting_metricmap[main_metric],
          facet_col = ifelse(length(sites) > 1, "Site", ""),
          facet_row = ifelse(length(models) > 1, "model", ""),
        )
      print(ba)
      ggsave(filename = file.path(fig_dir, paste0("ba_", fig_suffix)), plot = ba, width = fig.sizes[1], height = fig.sizes[2])
      ggsave(filename = file.path(fig_dir, paste0("ba_pred_obs_", fig_suffix)), plot = (pred_obs + ba), width = fig.sizes[1]*2 - 1, height = fig.sizes[2])
      list(
        pred_obs = pred_obs,
        ba = ba
      )      
    },
    SIMPLIFY = FALSE
  )

pred_obs_freising <- pred_plots[[2]]$pred_obs
pred_obs_score_summary <- ggarrange(pred_obs_freising, score_summary, widths = c(4,8), labels = c("A", "B"))
pred_obs_score_summary

ggsave(file = file.path(fig_dir, "pred_obs_score_summary.pdf"), plot = pred_obs_score_summary, width = 12, height = 6)

Explained Variance Selected Features on Freising

require(ggrepel)

## Loading required package: ggrepel

selected_lm_fits <- sapply(new_models,
       function(model) {
         lm_fit <- model |> extract_fit_engine()
         coef_mat <- lm_fit |> summary() |> coefficients()
         # coef_mat[coef_mat[, 'Pr(>|t|)'] < 0.05, , drop = FALSE] |> print()
         lm_fit
       }, simplify = FALSE)

feature_imps <- c("lmg", "pmvd")
linear_imp <- relaimpo::calc.relimp(selected_lm_fits$selected_linear, type = feature_imps)
expl_variance <- data.table::setDT(enframe(c(linear_imp$pmvd, `Intra-Individual Variation` = 0.043, Unexplained = 0), 'Feature', 'Explained Variance'))
expl_variance[Feature == 'Unexplained', `Explained Variance` := 1 - sum(expl_variance$`Explained Variance`)]
expl_variance[, Feature:=factor(Feature, levels=c(names(sort(linear_imp$pmvd, decreasing = TRUE)), 'Unexplained', 'Intra-Individual Variation'))]
data.table::setkey(expl_variance, Feature)
expl_variance[, cum_var := cumsum(`Explained Variance`)]
expl_variance[, x_space := cum_var - `Explained Variance`/2]

expl_variance_plot <- ggplot(expl_variance, aes(x = `Explained Variance`, y = 'Feature', fill = reorder(Feature, -x_space))) + 
    geom_col(position = 'fill') + 
    scale_fill_manual(values = feature_colors, guide = guide_legend(reverse = TRUE, nrow = 1)) + 
    theme(axis.text.y = element_blank(), axis.ticks.y = element_blank(), legend.position = 'top') + 
    ggrepel::geom_label_repel(aes(label = round(`Explained Variance` * 100, 1),
                                  x = x_space),
                              max.overlaps = 10,
                              min.segment.length = 0,
                              force = 10,
                              direction = 'y',
                              show.legend = FALSE,
                              color = text_colors[expl_variance[, levels(Feature)]],
                              segment.color = text_colors[expl_variance[, levels(Feature)]]) + 
    labs(y = NULL, fill = NULL)
ggsave(filename = file.path(fig_dir, "selected_features_expl_variance.pdf"), plot = expl_variance_plot, width = 8.5, height = 3)

Data Plots

scatter <- ggscatterhist(all_data, x = "Mean Outdoor Temperature", y = "RMR", color = "Site", xlab = "Mean Daily Temperature in °C", ylab = "RMR in kJ", alpha=.5, print = FALSE, legend = "bottom")
scatter$sp <- scatter$sp + geom_smooth(method = 'lm', se = FALSE, aes(color = Site)) + stat_cor(size = 3, aes(color = Site))
pdf(file.path(fig_dir, "scatter_temp_rmr.pdf"), width = 7, height = 7)
scatter

## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'

dev.off()

## png 
##   2

print(scatter)

## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'

scatter_kiel_scores <- ggpubr:::.insert_xaxis_grob(scatter$sp, scatter$xplot, grid::unit(1/5, 
                                                "null"), position = "top")

## `geom_smooth()` using formula = 'y ~ x'

scatter_kiel_scores <- ggpubr:::.insert_yaxis_grob(scatter_kiel_scores, scatter$yplot, grid::unit(1/5, 
                                                 "null"), position = "right")
scatter_kiel_scores <- ggarrange(as_ggplot(scatter_kiel_scores), score_summary_kiel, labels = c("A", "B"))
ggsave(filename = file.path(fig_dir, "scatter_temp_rmr_kiel_scores.pdf"), plot = scatter_kiel_scores, width = 14, height = 7)

library(pheatmap)
library(seriation)
cor_method <- "pearson"
cor_mat <-
  general_recipe |> step_select(c(all_predictors(), all_outcomes())) |> prep() |> bake(NULL) |> cor(use = "pairwise", method = cor_method)
colnames(cor_mat)[colnames(cor_mat) == "Sex_weiblich"] <- "Sex (f)"
rownames(cor_mat)[rownames(cor_mat) == "Sex_weiblich"] <- "Sex (f)"

write.table(round(cor_mat[order(cor_mat[, "RMR"], decreasing = TRUE), "RMR", drop=FALSE], 3), quote=FALSE, sep=',')

## RMR
## RMR,1
## FFM,0.853
## Weight,0.722
## Height,0.706
## Hemoglobin,0.538
## Waist,0.493
## Hematocrit,0.484
## Uric Acid,0.471
## Visceral Fat,0.456
## MCHC,0.422
## fT3,0.404
## Hip,0.349
## GPT ALT,0.343
## Creatinine,0.334
## Ferritin,0.281
## Triglycerides,0.279
## GGT,0.251
## BP Diastolic,0.247
## Iron,0.204
## GFR,0.203
## BP Systolic,0.199
## propionic acid a,0.187
## Glucose,0.185
## FM,0.182
## GOT AST,0.171
## f__Sutterellaceae,0.16
## Insulin,0.159
## f__Prevotellaceae,0.135
## f__unknown_ Bacteroidetes,0.129
## butyric acid a,0.12
## f__Succinivibrionaceae,0.111
## f__Acidaminococcaceae,0.107
## f__Coriobacteriaceae,0.103
## f__Erysipelotrichaceae,0.101
## Urea,0.099
## acetic acid a,0.074
## f__Enterococcaceae,0.073
## f__Veillonellaceae,0.066
## Leukocytes,0.059
## f__Lachnospiraceae,0.052
## Body Temperature,0.051
## TSH,0.043
## f__Pasteurellaceae,0.037
## Heart Rate,0.035
## f__Comamonadaceae,0.035
## f__Clostridiaceae 1,0.035
## f__Rhodospirillaceae,0.033
## f__Enterobacteriaceae,0.032
## Isobutyrate a,0.022
## f__Fusobacteriaceae,0.017
## f__Bifidobacteriaceae,0.014
## f__Peptococcaceae 1,0.011
## Isovalerate a,0.002
## LDH,-0.002
## f__Eubacteriaceae,-0.003
## 2-Methylbutyrate a,-0.005
## pentanoic acid a,-0.009
## f__Peptostreptococcaceae,-0.01
## f__Spirochaetaceae,-0.011
## Lactic acid a,-0.019
## f__Lactobacillaceae,-0.022
## 4-Methylvaleric acid a,-0.028
## f__unknown_ Desulfovibrionales,-0.032
## f__Methanobacteriaceae,-0.036
## f__unknown_ Rhodospirillales,-0.036
## f__Puniceicoccaceae,-0.038
## LDL,-0.038
## hexanoic acid c,-0.039
## f__Bacteroidaceae,-0.042
## f__unknown_ Proteobacteria,-0.057
## hsCRP,-0.058
## f__Streptococcaceae,-0.061
## f__unknown_ Alphaproteobacteria,-0.064
## f__Victivallaceae,-0.07
## f__unknown_ Burkholderiales,-0.072
## f__unknown_ Clostridia,-0.072
## f__Elusimicrobiaceae,-0.078
## f__Desulfovibrionaceae,-0.082
## f__Verrucomicrobiaceae,-0.097
## f__unknown_ Bacteroidales,-0.1
## f__Anaeroplasmataceae,-0.104
## f__unknown_ Deltaproteobacteria,-0.104
## f__unknown_ Bacteria,-0.122
## Simpson.effective,-0.128
## f__unknown_ Firmicutes,-0.136
## Shannon.effective,-0.147
## Mean Outdoor Temperature,-0.147
## f__unknown_ Clostridiales,-0.156
## f__Rikenellaceae,-0.174
## Age,-0.184
## f__Ruminococcaceae,-0.188
## Cholesterol,-0.199
## f__Porphyromonadaceae,-0.219
## HDL,-0.49
## Sex (f),-0.658

microbiome_cor_mat <- round(cor_mat[column_groups[group %in% c("microbiome family", "microbiome diversity"), column], "RMR", drop = FALSE], 3)
microbiome_cor_mat <- microbiome_cor_mat[order(microbiome_cor_mat[, "RMR"], decreasing = TRUE), , drop=FALSE]
colnames(microbiome_cor_mat)[colnames(microbiome_cor_mat) == "RMR"] <- "RMR (kJ/day)"
write.table(microbiome_cor_mat, quote = FALSE, sep = ',')

## RMR (kJ/day)
## f__Sutterellaceae,0.16
## f__Prevotellaceae,0.135
## f__unknown_ Bacteroidetes,0.129
## f__Succinivibrionaceae,0.111
## f__Acidaminococcaceae,0.107
## f__Coriobacteriaceae,0.103
## f__Erysipelotrichaceae,0.101
## f__Enterococcaceae,0.073
## f__Veillonellaceae,0.066
## f__Lachnospiraceae,0.052
## f__Pasteurellaceae,0.037
## f__Clostridiaceae 1,0.035
## f__Comamonadaceae,0.035
## f__Rhodospirillaceae,0.033
## f__Enterobacteriaceae,0.032
## f__Fusobacteriaceae,0.017
## f__Bifidobacteriaceae,0.014
## f__Peptococcaceae 1,0.011
## f__Eubacteriaceae,-0.003
## f__Peptostreptococcaceae,-0.01
## f__Spirochaetaceae,-0.011
## f__Lactobacillaceae,-0.022
## f__unknown_ Desulfovibrionales,-0.032
## f__Methanobacteriaceae,-0.036
## f__unknown_ Rhodospirillales,-0.036
## f__Puniceicoccaceae,-0.038
## f__Bacteroidaceae,-0.042
## f__unknown_ Proteobacteria,-0.057
## f__Streptococcaceae,-0.061
## f__unknown_ Alphaproteobacteria,-0.064
## f__Victivallaceae,-0.07
## f__unknown_ Burkholderiales,-0.072
## f__unknown_ Clostridia,-0.072
## f__Elusimicrobiaceae,-0.078
## f__Desulfovibrionaceae,-0.082
## f__Verrucomicrobiaceae,-0.097
## f__unknown_ Bacteroidales,-0.1
## f__Anaeroplasmataceae,-0.104
## f__unknown_ Deltaproteobacteria,-0.104
## f__unknown_ Bacteria,-0.122
## Simpson.effective,-0.128
## f__unknown_ Firmicutes,-0.136
## Shannon.effective,-0.147
## f__unknown_ Clostridiales,-0.156
## f__Rikenellaceae,-0.174
## f__Ruminococcaceae,-0.188
## f__Porphyromonadaceae,-0.219

non_microbiome_cor_mat <- round(cor_mat[!rownames(cor_mat) %in% rownames(microbiome_cor_mat), "RMR", drop = FALSE], 3)
non_microbiome_cor_mat <- non_microbiome_cor_mat[order(non_microbiome_cor_mat[, "RMR"], decreasing = TRUE), , drop=FALSE]
colnames(non_microbiome_cor_mat)[colnames(non_microbiome_cor_mat) == "RMR"] <- "RMR (kJ/day)"
write.table(non_microbiome_cor_mat, quote = FALSE, sep = ',')

## RMR (kJ/day)
## RMR,1
## FFM,0.853
## Weight,0.722
## Height,0.706
## Hemoglobin,0.538
## Waist,0.493
## Hematocrit,0.484
## Uric Acid,0.471
## Visceral Fat,0.456
## MCHC,0.422
## fT3,0.404
## Hip,0.349
## GPT ALT,0.343
## Creatinine,0.334
## Ferritin,0.281
## Triglycerides,0.279
## GGT,0.251
## BP Diastolic,0.247
## Iron,0.204
## GFR,0.203
## BP Systolic,0.199
## propionic acid a,0.187
## Glucose,0.185
## FM,0.182
## GOT AST,0.171
## Insulin,0.159
## butyric acid a,0.12
## Urea,0.099
## acetic acid a,0.074
## Leukocytes,0.059
## Body Temperature,0.051
## TSH,0.043
## Heart Rate,0.035
## Isobutyrate a,0.022
## Isovalerate a,0.002
## LDH,-0.002
## 2-Methylbutyrate a,-0.005
## pentanoic acid a,-0.009
## Lactic acid a,-0.019
## 4-Methylvaleric acid a,-0.028
## LDL,-0.038
## hexanoic acid c,-0.039
## hsCRP,-0.058
## Mean Outdoor Temperature,-0.147
## Age,-0.184
## Cholesterol,-0.199
## HDL,-0.49
## Sex (f),-0.658

write.table(cor_mat, quote = FALSE, sep = ',')

## Age,Mean Outdoor Temperature,Height,Weight,FM,FFM,Visceral Fat,Waist,Hip,Body Temperature,Leukocytes,hsCRP,Insulin,TSH,fT3,Hemoglobin,Hematocrit,MCHC,GOT AST,GPT ALT,GGT,LDH,Glucose,Cholesterol,Triglycerides,HDL,LDL,Creatinine,GFR,Urea,Uric Acid,Iron,Ferritin,BP Systolic,BP Diastolic,Heart Rate,acetic acid a,butyric acid a,propionic acid a,2-Methylbutyrate a,hexanoic acid c,Isobutyrate a,Isovalerate a,pentanoic acid a,4-Methylvaleric acid a,Lactic acid a,f__Acidaminococcaceae,f__Anaeroplasmataceae,f__Bacteroidaceae,f__Bifidobacteriaceae,f__Clostridiaceae 1,f__Comamonadaceae,f__Coriobacteriaceae,f__Desulfovibrionaceae,f__Elusimicrobiaceae,f__Enterobacteriaceae,f__Enterococcaceae,f__Erysipelotrichaceae,f__Eubacteriaceae,f__Fusobacteriaceae,f__Lachnospiraceae,f__Lactobacillaceae,f__Methanobacteriaceae,f__Pasteurellaceae,f__Peptococcaceae 1,f__Peptostreptococcaceae,f__Porphyromonadaceae,f__Prevotellaceae,f__Puniceicoccaceae,f__Rhodospirillaceae,f__Rikenellaceae,f__Ruminococcaceae,f__Spirochaetaceae,f__Streptococcaceae,f__Succinivibrionaceae,f__Sutterellaceae,f__unknown_ Alphaproteobacteria,f__unknown_ Bacteria,f__unknown_ Bacteroidales,f__unknown_ Bacteroidetes,f__unknown_ Burkholderiales,f__unknown_ Clostridia,f__unknown_ Clostridiales,f__unknown_ Deltaproteobacteria,f__unknown_ Desulfovibrionales,f__unknown_ Firmicutes,f__unknown_ Proteobacteria,f__unknown_ Rhodospirillales,f__Veillonellaceae,f__Verrucomicrobiaceae,f__Victivallaceae,Shannon.effective,Simpson.effective,Sex (f),RMR
## Age,1,0.117136070023207,-0.238184677355795,0.179554881266403,0.412919637889792,-0.113773911026149,0.501566058311765,0.441542399915113,0.175324691090086,-0.263289348129292,-0.0417830760812068,0.132674377841552,0.208050243439315,-0.0888702552783854,-0.292264792006971,0.0141967705540277,0.0296532571162853,-0.030498307993227,0.0068628531818738,0.00227465656323271,0.205157072208608,0.198845017852987,0.283680625149849,0.419080711440776,0.122066591678719,0.0702688024352788,0.384316792093568,0.0764022604319091,-0.773223135423936,0.398944975516159,0.228591516852409,-0.195736899877867,0.359416365464615,0.543066770941934,0.37882448087062,-0.0421958205140314,-0.0395957799425808,-0.135369553886164,-0.093233876745631,-0.0482196553660839,0.0540636063973095,-0.0778733189869173,-0.0143129327619469,0.0376066163563243,0.0529882061204608,-0.125863869590178,-0.0337628825130373,0.0186063272937989,-0.0522550408000946,-0.193174577276283,0.138148427168631,-0.0517797425728952,0.118385766876458,-0.00759536938761584,0.089878278705156,0.181970598676747,0.0746091327980739,0.0655027300127757,-0.0991231533981136,-0.019378926678712,0.00420369187902849,0.102336131799964,0.12419601555717,-0.16329387396517,0.177076875821884,0.0757992301130971,0.0786829883769361,-0.0144274602045589,0.027012732216533,-0.0604942456736317,0.0561703655717665,-0.0444750047358489,0.0248087193068966,0.0569513820577947,-0.0150750583081717,-0.0635593153937235,-0.02738763437379,0.070695933647106,-0.0212742791134975,0.0201536422231337,-0.0126506164351598,0.0141386101393679,0.156764949799439,-0.0142489503545086,0.0617759031714565,0.0579856702810597,-0.036629614976783,0.107333647484019,-0.0548827053033902,0.068030286075855,0.0397160897827812,0.118744178965278,0.080644555290159,-0.0595777470409746,-0.184412759666658
## Mean Outdoor Temperature,0.117136070023207,1,-0.02188461352544,0.111921415410402,0.10867094562226,0.0608794164812004,0.157830132392411,0.110386113306691,0.0379559017353788,-0.149912195450489,-0.0870012437496399,0.0165505392697393,0.0797896068653561,-0.0596604143096942,-0.155567578598379,-0.0785990930082974,-0.0676184459812008,-0.0730995031678947,0.0760176145727991,0.105527932537722,0.104850789299202,0.0985922976642754,0.137720638612295,0.0501717878975772,0.104546321034675,-0.000625052177099107,0.0184188989312026,0.000162985858482369,-0.0972552098142298,0.0122565910869697,0.0452266009164798,-0.073643433446511,0.105447362933263,-0.0933911473989838,-0.0400749754068231,0.00862288563940877,0.0349184585280418,-0.0692506079782795,0.0127264695258399,-0.030596251056701,-0.0179228125013649,-0.0570555908215686,-0.0311441641724398,0.00834330605919268,-0.0288857168809748,-0.186332160473881,-0.0430273749007414,0.071363695597394,0.0541145070457822,0.0174769576625724,-0.0243069549714157,-0.081918493357533,0.0740901018368149,0.0604704628338058,-0.0464943363009956,-0.0447806217175891,-0.0818367766961119,0.132973671042216,0.00245408680842686,0.0405445742215562,-0.010628462018208,-0.0067644490751317,-0.00508122324402333,-0.0200146149733645,0.158174200032969,-0.0548314086739511,0.00992038525693417,-0.00945905847825129,-0.03268066377528,-0.00951180426372413,0.0382749930015863,-0.0542777264139824,0.00848115426529179,-0.00319682360840291,0.0652161449689048,0.095630122875979,-0.0118522375811793,-0.0855278974388435,-9.85030097477337e-05,-0.0414043648689914,-0.0250280583420901,0.00656090936293092,-0.101299296985294,0.0454125347061092,-0.0433539522828248,-0.113979454141089,0.00095806542812103,-0.000952125098733892,0.0430038358860277,2.65047533915927e-05,0.0153568572640554,-0.0426670117438889,-0.0432720956505935,0.00346011792904233,-0.147487047870104
## Height,-0.238184677355795,-0.02188461352544,1,0.527484872668396,-0.102848897944633,0.831689176945207,0.233185100228519,0.222724614558442,0.0709102239126728,-0.054961936579401,-0.107198758995122,-0.0731214383446551,-0.00910492188106908,0.0800904897821533,0.290099562291734,0.463070453906779,0.432506676617067,0.321941326326147,0.153078314146545,0.270752883760424,0.239055767848824,-0.0463781214016796,0.058948951956477,-0.278875541166133,0.11658975283042,-0.430591425781593,-0.13993889872077,0.382096901504131,0.213738870534483,0.0707031777731027,0.380521819790287,0.193451760892118,0.233428241008525,0.0486775354520486,0.0483587203823246,-0.104647072844746,0.0150336661537965,0.12389382527992,0.0953695623264191,-0.0411071805097411,0.0163121655077653,-0.0330228951253012,-0.0398351926308116,-0.0267833479018829,0.0213014698584518,-0.0131002924315167,0.00716381043062184,-0.134304878006228,-0.0481506216049491,0.00563437888385382,0.016546185103386,0.0386503483556719,0.0310945600900611,-0.060308937734133,-0.0701828512046352,0.0296887354885645,0.0649658601775982,0.0348836532423152,0.0466966645383628,0.00798386505417687,0.028387548579066,-0.0321096212603754,-0.0599585615411254,0.0590590647445305,0.0303009682063023,-0.0463494672122576,-0.0788199471001303,0.124217912738868,-0.0421820864116248,0.0190711535329903,-0.0972253458763538,-0.0754401661333538,-0.0507969969555556,-0.043675900952457,0.0370557969631341,0.12700073790142,-0.0801960776719285,-0.111247675395206,-0.0667046900954158,0.0716788947789419,-0.0423362429151389,-0.0824629801110609,-0.0967293547385683,-0.042624357738487,-0.0117524746225325,-0.0529789508436558,0.00443126291821354,0.00107872237990128,0.0650844642702941,-0.0581851267002705,-0.0743855794651706,-0.0849658074386007,-0.0886374362809392,-0.697779169208974,0.706292450492882
## Weight,0.179554881266403,0.111921415410402,0.527484872668396,1,0.705860199077756,0.778569916914055,0.800277389997174,0.873997180183502,0.756153964154566,-0.0518090725924663,0.0668312065170515,-0.0166004539048817,0.440274228768211,0.0187194798128741,0.174017159071276,0.411800406653968,0.386837015962775,0.281530590566103,0.134133927085319,0.402418627839598,0.365634539154521,0.0730021351702585,0.356205184473739,-0.00042168585321633,0.443673556422739,-0.540837062678497,0.17755440232586,0.319150795191466,-0.134028788452365,0.175678578637618,0.571155796893899,0.0623255500110475,0.446512304989,0.278747046641116,0.380423835836508,0.039406685485827,0.0910620437868223,0.0930560484811709,0.192191180670079,-0.0216145526750559,-0.0225043056104213,0.00337946968814554,-0.00300641087081474,0.0558519243380635,-0.0124248648961408,-0.0857434972517397,0.119608751177056,-0.120127824997846,-0.016259705291953,-0.0566862243979485,0.0762756026979748,0.0160698753957377,0.178535477352727,-1.32285965806866e-05,-0.0294379466731168,0.119857920529856,0.108061669033868,0.0666359342695937,-0.0269498446019051,0.0152526656409665,0.044728027863273,0.00747290905910186,0.0056300178363687,-0.0868664450314965,0.105145683411328,0.0164536815617315,-0.157624224774542,0.13906321094518,-0.0620410089375208,0.00128718647794843,-0.132201952902437,-0.20541143500203,-0.0805429607196762,-0.0258220670471097,0.04788152132107,0.138914285486151,-0.0877143391339524,-0.143835709522316,-0.128313148548098,0.106058039455546,0.00666337550557607,-0.0726343769902047,-0.167711442175838,-0.0949655159710579,0.0371704550006995,-0.152861420296728,-0.0943408155877271,0.0381255094610412,0.0616604681263811,-0.0698948531314221,-0.0704804173314743,-0.128363524932325,-0.131912564558257,-0.509747996654153,0.722217338567701
## FM,0.412919637889792,0.10867094562226,-0.102848897944633,0.705860199077756,1,0.105030261950283,0.695958923406292,0.791480274974698,0.883495867501317,-0.0127609970056902,0.182147571556185,0.0814196219857618,0.531746520324084,-0.0121713165457863,-0.118370619113885,-0.014295995120648,-0.0133593129001342,-0.00539492823815049,-0.00139580276918877,0.19704472936774,0.220519595766695,0.107763541961226,0.326856118021896,0.244460144720276,0.388698188723157,-0.233006993262197,0.329839061167443,-0.0710381521311265,-0.326542815999053,0.0887884749897682,0.288061828591242,-0.114219599369008,0.297020189486699,0.245104236550589,0.39517586561208,0.169250570491403,-0.00621392164138514,-0.0654708551713756,0.0420300962760202,-0.0180582545486415,-0.0433906040582158,-0.00563722619364213,9.61623715814834e-05,0.0426182996157321,-0.0369949028764589,-0.109323889975839,0.0682119965491398,-0.0646050954356582,0.000557339384527073,-0.0682653706144379,0.0382222161983315,0.010686406370985,0.149381529311101,0.0665092724888446,0.0445116380397581,0.119820373562031,0.0817814110815954,0.0325087006623424,-0.0608169806172322,0.0108547635704362,0.0315651108247167,0.0350175682500291,0.0807345704206555,-0.155165739331661,0.109211608846562,0.039282413685541,-0.0468884163429348,0.0497871156884102,-0.0234736366716436,-0.0741284524220232,-0.0279442323738742,-0.12633687492358,-0.0523487083363685,0.0226971372245904,-0.0114440454488191,0.0490783394135659,-0.0241333411683492,-0.0464134271875209,-0.0881738082096117,0.0414475447407864,0.06586607890722,0.0125860945675021,-0.0735385339173505,-0.0513140742417067,0.0838088470744732,-0.0754422060527611,-0.146179196982006,0.0865147373810685,0.0233298962374974,0.0102546224270369,-0.0200398481306225,-0.0237637954658437,-0.026579650622505,0.132182725145674,0.181632132486318
## FFM,-0.113773911026149,0.0608794164812004,0.831689176945207,0.778569916914055,0.105030261950283,1,0.506912390158947,0.52579350053558,0.278859040759938,-0.0614518751906617,-0.0675759589331424,-0.0954781667334844,0.14700715206305,0.0370708577432976,0.349215069530295,0.590786765486552,0.554897667522373,0.400053899064026,0.189580233317515,0.390417390252658,0.317951139343624,0.00701237698591976,0.210489582663457,-0.217147105617662,0.27854218238333,-0.552867351970312,-0.042923086856529,0.510972285721626,0.101167237829264,0.167983903977035,0.546646462619201,0.188719229315117,0.363742127300706,0.174194380042852,0.184007606215157,-0.0946329568639018,0.133367305864791,0.188659174439262,0.232597577704909,-0.0143262878503184,0.00683706269378284,0.00975431527903456,-0.00428773589154429,0.0406572476059164,0.0153229602696807,-0.0235500814728665,0.107479601967639,-0.111411487011282,-0.0233467810601134,-0.0190787122204673,0.0732363025429348,0.013095422665841,0.118340906585043,-0.0589406412757896,-0.0807628873922546,0.0620424257013307,0.0792418449813038,0.0647734223614068,0.0160489701318912,0.0117990459669366,0.0348605700252052,-0.0205278470816139,-0.0636138520547627,0.0155225877918395,0.0508690832776129,-0.0116844335999772,-0.179809795324161,0.151123380252393,-0.0662992572524288,0.067492697621424,-0.160862849048586,-0.176440319086062,-0.0666986893620877,-0.056344952299167,0.0773636960952037,0.151526882432516,-0.101770827006594,-0.16080188541736,-0.102034403414214,0.112183594075227,-0.0489878551538031,-0.113122513001675,-0.170276892697067,-0.0878512678633732,-0.0220600835205295,-0.147761238089637,-0.00293877769029672,-0.0231124006704273,0.0659245675236489,-0.107230252246607,-0.0811871403144304,-0.159167943007718,-0.161647073114767,-0.832744630502507,0.853038725917889
## Visceral Fat,0.501566058311765,0.157830132392411,0.233185100228519,0.800277389997174,0.695958923406292,0.506912390158947,1,0.92865415883772,0.564045462454043,-0.0807480511660292,0.0994193629902282,0.0154797807915235,0.500078347844408,-0.0201226517370349,0.0731125103843921,0.335642540840339,0.329248061122573,0.190075947076712,0.10170590910455,0.367285319001965,0.432310844576284,0.11950088341001,0.451388534221424,0.168273235082714,0.46604992124161,-0.403956203160037,0.304504624618962,0.275251626086776,-0.357849640102507,0.251965680728531,0.603446617682579,-0.0168489361615362,0.573585993835659,0.398179032579535,0.395924035666075,0.0650285221188822,0.069138194130598,0.0368509190235835,0.161575182731451,-0.0253642635663647,-0.011104502814807,-0.0229200231701553,0.00270142313887912,0.0999665828348479,-0.00227095819273064,-0.109277316566205,0.0495973274845004,-0.0993360164597002,0.0184684954717301,-0.122656005236056,0.125298687473909,-0.0572959575338634,0.146695208271347,-0.0229561975907965,0.0211433589745846,0.205927930747735,0.141516559008156,0.105981686803877,-0.0822309972619255,0.0182231982876225,0.0402248712454606,0.0822202301746684,0.0362557529197629,-0.133706202394918,0.17034557920541,0.0323505065939346,-0.123366188686556,0.0747318094986228,-0.083629560426703,-0.0414593943159861,-0.113779446211433,-0.251156998188936,-0.0424382168257206,0.0240041991919493,-0.0133483498476516,0.0866736989747385,-0.0480937869268088,-0.133740740670018,-0.0943038979479018,0.0580197375936793,-0.00183502916694229,-0.0319865724723312,-0.146096366236215,-0.116896529994423,0.0595629099486169,-0.160425997430756,-0.0958336452637264,0.0317860318240314,0.0629935454175333,-0.0308293785837023,-0.0628971562242779,-0.108097106474971,-0.113635984590586,-0.454822907508006,0.456396095509878
## Waist,0.441542399915113,0.110386113306691,0.222724614558442,0.873997180183502,0.791480274974698,0.52579350053558,0.92865415883772,1,0.724324433127591,-0.0394217975779049,0.109372263371186,0.0405128164606869,0.515372841353239,-0.013793475993117,0.0710339704378507,0.318361625032318,0.307426669340642,0.194509514734655,0.0528649940809604,0.330578767686959,0.367080913990194,0.0893413475946097,0.415467134093191,0.14345494803598,0.456260704543932,-0.446734229916899,0.298626520517979,0.221778530263176,-0.309020074507521,0.219069342120492,0.563208620235801,-0.0112629664497649,0.496579015124054,0.394910534103513,0.447439651380319,0.0722903484495167,0.101671289952802,0.058602352464058,0.197079811857077,-2.49381498907089e-05,-0.0193256371589784,0.00197625668272699,0.0229053019202854,0.0998233176167243,-0.00907694858924787,-0.0749141369559419,0.0840487922138004,-0.101043024812114,0.0270683165582608,-0.071442076514652,0.0992984293683952,-0.00730144788625091,0.15261302783455,-0.0332478646506824,0.030582537230887,0.184363724936843,0.11597805801731,0.0699428759048154,-0.0646275074094075,0.0127259269777173,0.0793444394953758,0.0650969376430923,0.0148393968133001,-0.132745870476716,0.130191549768013,0.0392976280489812,-0.153179934281747,0.0799261592423149,-0.0711480781683402,-0.0597982400704054,-0.118396232873707,-0.226107881591928,-0.0666193463063618,0.00616841433147701,0.000915829582542574,0.0681408115837627,-0.0751840449873312,-0.149548523999952,-0.111610813448538,0.0625949260885474,0.0537780109642693,-0.0312575183389046,-0.143526770732447,-0.123345723160709,0.0619109750343958,-0.155653528528066,-0.101045270453363,0.0278367915429846,0.0426713641243096,-0.054496637301595,-0.0439446238932288,-0.114327220232302,-0.116040773296618,-0.380763182671027,0.492854323111926
## Hip,0.175324691090086,0.0379559017353788,0.0709102239126728,0.756153964154566,0.883495867501317,0.278859040759938,0.564045462454043,0.724324433127591,1,0.07513702683343,0.180921680546343,0.0514831712027525,0.471959999516172,-0.00656730046203911,-0.0120107713693493,0.0579716519936824,0.0534395455217346,0.0466859008306633,0.0253244264169662,0.188969834361624,0.168310020170097,0.082175086314222,0.240221548032631,0.075997041641552,0.325447293309578,-0.268516281564376,0.17512696970141,-0.0143881086448218,-0.142163982391671,0.026597106397664,0.284939242935086,-0.0674341532605858,0.232125759508358,0.168590615350702,0.33481216012119,0.138709161762108,0.052000867405524,0.0125610801939082,0.0903219662255707,-0.00343024980709604,-0.0339647782128689,0.0240050688106408,0.00807360952260146,0.039641150898218,-0.0268786402062031,-0.0525117491961227,0.109774508964473,-0.0822279420303432,-0.0222520286382176,-0.00595055101567017,0.0401137865131812,0.077750763288167,0.113408356507964,0.0314629491061929,0.067990671038214,0.0922800791374516,0.058888358384972,0.0243269319542427,-0.0339645279396524,0.0187239821824269,0.0603244977783849,0.0217850332564755,0.0391784088787951,-0.0837690532098565,0.0532540124475117,0.0571455088426617,-0.100982487514695,0.0799138531236695,-0.0513807444998264,-0.0660558789970037,-0.0843566640036723,-0.084161422611955,-0.0752672178340444,0.021389175847448,0.0132087565848616,0.0360219989827204,-0.0382285370382374,-0.0647585099883699,-0.0879007674556568,0.0544464435252283,0.0737609126844342,0.0236401032086536,-0.0681253697119656,-0.0740287767397988,0.0110678907335948,-0.0888904862459868,-0.152747701319113,0.00572349770839562,0.0250089098046042,-0.0351990310067782,-0.0140774894222489,-0.0263117636267456,-0.0281089143232601,0.0368229352953622,0.349196998570865
## Body Temperature,-0.263289348129292,-0.149912195450489,-0.054961936579401,-0.0518090725924663,-0.0127609970056902,-0.0614518751906617,-0.0807480511660292,-0.0394217975779049,0.07513702683343,1,0.266170578319595,0.0460862893674874,0.0374313779098414,0.0398195410605527,0.0431219323894643,-0.124757813292413,-0.0999665699460659,-0.150067861876862,-0.191961467949873,-0.0896406677913927,-0.0549683519325389,-0.123307230540619,-0.0410214419662869,-0.189525944304483,0.0162070973625027,-0.0123150765672222,-0.176653148000709,-0.115123400084088,0.222662764474371,-0.241720923510282,-0.0373001497763412,-0.024647723099651,-0.157918580140953,-0.106143985799144,-0.112979356849165,0.236991085734166,0.109664809415007,0.142608082448957,0.145994204479597,0.0653214431313893,-0.0460103689172076,0.07335035204823,0.0560614785016914,0.0821499693071723,-0.0489221731470889,0.107207586065744,-0.00716916000131398,0.0275188433633268,0.0485434131373882,0.0471423362156049,-0.00155248206679331,0.10219596798906,-0.127511097993397,-0.0519861288888768,0.00142405229544252,-0.0403110634488636,-0.0204662937793099,-0.0227398351396724,0.0374307656290237,0.0212942762385343,0.0723238315275669,-0.0149961405859896,0.0193773327962213,0.0188291109405007,-0.00643438294104965,-0.0554807604393902,-0.0820732001525535,-0.0439752867383649,-0.0220278903284479,-0.0503760700359643,-0.00755265753276471,0.00677257135560326,-0.0620779429469439,-0.0123249225116542,-0.0268648190391321,-0.0102332948649083,0.107767665891346,-0.0428922828216581,0.0119372487405395,-0.0900816382080169,0.0247283838465716,-0.0121329576029897,-0.0336800618632054,0.0130647031061242,-0.00863826529135102,-0.0790694825918823,-0.0595364941628083,-0.102366824670969,-0.0394830410191565,-0.00625460105021475,0.0213687907097353,-0.03427268623384,-0.0261915165161485,0.137530872494534,0.0512902508975052
## Leukocytes,-0.0417830760812068,-0.0870012437496399,-0.107198758995122,0.0668312065170515,0.182147571556185,-0.0675759589331424,0.0994193629902282,0.109372263371186,0.180921680546343,0.266170578319595,1,0.218226978736497,0.203804086180748,-0.00525031970955907,0.060079238148677,0.0323986388325866,0.0545805198286561,-0.0487450321577057,-0.0874960696002911,-0.0589316018041604,0.0125372693860629,-0.0205447167164689,0.00683238328630066,-0.0777633853966827,0.205671672128691,-0.0754565104210603,-0.0346144934136852,-0.101680660338221,0.0384774893271003,-0.123062770017209,0.101120616609972,0.0372267935902959,0.00813845581016593,-0.0651683032121103,-0.0420406472048182,0.199575649072421,0.0524385076693959,0.0414754844781804,0.0596214765427855,-0.057536348971791,-0.0302142299323346,-0.0440981878088322,-0.0537296337566022,0.00401166834255727,-0.023531776360098,0.0872300071541129,0.0170514023344768,-0.102163875903231,0.0906918314683662,0.0715117411491055,-0.073898161068756,-0.0550946298177433,-0.0797547071177506,-0.142018469415062,0.00984433673967013,0.012850915172072,-0.0815007734412401,0.0744393306178747,-0.0243116711907181,0.0362347507155954,0.0958457123486764,-0.00518897374084252,-0.01792141238023,0.0195355551686467,-0.00324853295496481,-0.0636825659326607,-0.0605007273776401,-0.0926311707303838,-0.0918795747108163,-0.0736281407541809,-0.0130242666047919,-0.0757478364255077,-0.00190097332602013,0.0598063819851072,0.00284694761335013,0.0536379945745382,-0.0464678476152275,-0.0272992149206293,-0.131011976441311,-0.0170095353934039,-0.0360760037383968,-0.0236691842364022,-0.130518505149291,-0.0267100862156475,-0.00336258810591843,-0.134684250797498,-0.0821799826199814,0.000314900905676963,0.0134215991606647,0.0305567612308509,-0.0073095022557472,-0.106400266288141,-0.0548851182810317,0.137909091633462,0.0588271686904903
## hsCRP,0.132674377841552,0.0165505392697393,-0.0731214383446551,-0.0166004539048817,0.0814196219857618,-0.0954781667334844,0.0154797807915235,0.0405128164606869,0.0514831712027525,0.0460862893674874,0.218226978736497,1,0.0294844122463378,0.00927208194055535,-0.206110846318345,-0.175072001125663,-0.176520564259761,-0.089138771151224,-0.0444104736678964,-0.0519458088237887,0.00827509417417852,0.0688537169031303,0.0533881465818769,-0.0483373545044591,-0.0268310314130251,0.0402452527079404,-0.0465972151685315,-0.122766853380673,-0.063296402481825,-0.0466691600208207,-0.0196261332465414,-0.167754236608827,0.0212590291999719,0.00515116226183895,0.00479461471942885,0.126795328373915,-0.0146035016671296,-0.0140640664965929,-0.0228437908477702,-0.0189867506304218,-0.0215133490120414,-0.0183127463888408,-0.01855819217265,-0.024732900578374,-0.0221351085456149,0.0126653328138571,-0.0308648293143876,-0.0289241402714478,-0.016335493465405,0.0305597051816608,0.0344810095533589,-0.00756764931575988,-0.0236071553335617,-0.0103018460590943,-0.00301203821874638,0.0210741051414892,0.000462187816987334,0.0279086425453212,-0.0212744993304822,0.0120511518526982,0.0265717948480859,0.179133522383794,-0.00484519155408051,0.019956677073065,-0.0115356394869563,0.0397753487484822,0.00539952031248569,-0.0190654125576936,-0.00165090182616862,-0.0267071771225193,0.00679862868794711,0.00252320264937307,-0.0112737020779349,-0.00853204573232631,-0.0129690407912231,0.00869068696803594,-0.00390432927123447,0.00519546520807276,-0.029118940625083,-0.00917024663271122,0.00334539710050104,-0.00897339201737536,-0.030024912791502,-0.0079942161867724,0.0134465847259518,-0.0213150844932326,-0.0106696902195912,0.0160896545027167,0.00460656675082397,0.0963312885990872,-0.0145943032201946,0.00518048139529498,0.00361172397425259,0.116654037029173,-0.0580417636820717
## Insulin,0.208050243439315,0.0797896068653561,-0.00910492188106908,0.440274228768211,0.531746520324084,0.14700715206305,0.500078347844408,0.515372841353239,0.471959999516172,0.0374313779098414,0.203804086180748,0.0294844122463378,1,0.0860184942971765,-0.00690712464599623,0.107930716799612,0.105626884514558,0.0586197138584825,0.0509710885662914,0.25667341825048,0.20573212118573,0.082603419856244,0.273696055288804,0.0913930954064238,0.390647845375906,-0.208629880118111,0.148209685732453,0.0961416290313474,-0.198515202690798,0.133078568656842,0.3314108521545,-0.033246299443423,0.338944069053123,0.120863054528532,0.181088102818473,0.122902819791154,0.0225453232869625,0.05884716101483,0.134542580050459,0.0346753746219812,-0.0189004999367869,0.0304525860125473,0.0282871578010044,0.0971550113053151,-0.017076045860082,-0.0976377555216196,-0.000294901587100465,-0.0375839491803616,0.0409177081090713,0.00996394952507883,-0.0347186041323222,-0.0475482346152791,0.0904885853764993,0.0517204784385947,-0.00383260706238327,0.0586479957624873,0.0114927080643651,0.0737191928888728,-0.0387498069794469,-0.0200287386685211,-0.000646529676798163,0.0544327189847429,-0.038503046867346,-0.0905747754278681,0.0287459788355536,-0.0357241375219536,-0.00584271415680949,0.0046801355713661,-0.101745442599396,-0.103460610220427,0.0213051917096819,-0.120278235077427,0.000547433100382012,0.0551466473529079,-0.0431227816755614,0.0661884400003094,-0.0241961942163217,-0.0715862466507157,-0.0708308657855504,-0.0544565881409054,0.0393827599452673,-0.0165127330242701,-0.129030344487903,-0.0417480127626138,0.0780041270714912,-0.136539573084584,-0.0730957722229454,0.11917633471665,0.0384158037734345,0.0895600172760087,-0.0651483890720279,-0.0561592738232624,-0.0463715659115747,-0.0247241407054695,0.159350394468411
## TSH,-0.0888702552783854,-0.0596604143096942,0.0800904897821533,0.0187194798128741,-0.0121713165457863,0.0370708577432976,-0.0201226517370349,-0.013793475993117,-0.00656730046203911,0.0398195410605527,-0.00525031970955907,0.00927208194055535,0.0860184942971765,1,0.0246077831280748,0.0475914999072129,0.0428992365354812,0.0315405466225083,-0.0566324321493582,0.0543724015620563,-0.0282196162913216,-0.0878744635128816,-0.00195688706595673,-0.0779355780526145,0.0940964677924821,-0.102521934893512,-0.0442588489686528,0.0726455550411794,0.0279604371480137,0.0346477067786679,0.0418019138087151,0.0908687922066465,0.040774841449757,-0.0357541415689929,-0.0539093700683251,0.000898143516818937,0.00317722621842317,0.000844744473399949,-0.0200966895907134,-0.0203614476286757,-0.00767519038396478,-0.0390605268073839,-0.0343078427634531,-0.0503598354671056,-0.00762799328647908,0.0124743320065695,-0.0122708997732285,-0.0122088219067264,-0.0659517025753285,0.0807767102589505,-0.0291820642977304,0.0557241754949542,-0.0179894586680445,-0.0302100696369932,-0.0592864700532673,-0.074776246014219,0.0237257429725414,0.0597661616626919,0.0344485086085207,-0.0532120374436797,0.0329453261591513,-0.0789004352863041,0.00702054789448725,0.0804240872694699,-0.0371799674039268,-0.057922531909495,-0.0353213839475453,0.00183966672956437,-0.0408386855843069,0.0058274144943517,-0.0621532884550938,0.058231334064541,-0.027327186531182,-0.0563412340083503,-0.0183890801584428,-0.039291307257633,-0.0772321076729572,0.00131217811585294,-0.000835923458772629,0.0198333387562507,0.0214321851064496,-0.0420747131779136,0.0385964250550266,-0.0530519037889053,-0.0479900939731942,-0.0067973464639144,-0.0455123015345965,-0.00796352725459156,-0.0111654042353362,0.0135595579024554,-0.0117435358012184,-0.0433921287709359,-0.0278592680877378,-0.0336976691683666,0.042920104187761
## fT3,-0.292264792006971,-0.155567578598379,0.290099562291734,0.174017159071276,-0.118370619113885,0.349215069530295,0.0731125103843921,0.0710339704378507,-0.0120107713693493,0.0431219323894643,0.060079238148677,-0.206110846318345,-0.00690712464599623,0.0246077831280748,1,0.342002974012503,0.324986055161574,0.225370511382947,0.00583708920732223,0.173075969238833,0.113081128090276,-0.131715721255636,-0.00672745560050004,-0.174942636976375,0.118541144405985,-0.306542592727523,-0.0789336791051191,0.206258316757017,0.268909154203561,0.00874079275017333,0.217885667090335,0.282237884922674,0.0860073000149713,0.0546114033240796,0.0852420865987778,0.071213077266803,0.155135955815847,0.180273810308132,0.17115496797889,-0.0846176714775511,-0.0477077213488395,-0.0367348359276858,-0.0864276099408317,-0.041340433093485,-0.0433975836250966,0.147140723825797,0.0461888350259286,-0.125105491260081,0.0461576350869307,0.120379728573839,0.0536827021000011,-0.0143606553725983,-0.0103258028216021,-0.0811141196820518,-0.0912154343592593,-0.0222202963931648,-0.0512477332783546,0.0962749240671107,-0.0180636591432608,-0.0300637305299972,0.100372492256625,0.000845857014178259,-0.0438425974823026,0.0912166269616079,0.00360408116073036,0.04904003480971,-0.180602836039801,-0.0713015471960358,-0.0377955955567833,0.0618920667039145,-0.13583767810858,-0.0434369172807135,-0.0066792129134107,-0.0694648955411959,0.0579932167006013,0.0747443707200723,0.0462527495305598,-0.157927746462342,-0.0679579322370015,0.0230113201017024,0.0524701865560724,-0.0341909081353208,-0.205853603861922,-0.0137696883760239,-0.0440913735697803,-0.125304071193874,-0.02085564142015,-0.101296448459335,0.0690204407118846,-0.234070734000742,-0.115889716851436,-0.133407060932367,-0.113722751755173,-0.389248797028189,0.404417523995975
## Hemoglobin,0.0141967705540277,-0.0785990930082974,0.463070453906779,0.411800406653968,-0.014295995120648,0.590786765486552,0.335642540840339,0.318361625032318,0.0579716519936824,-0.124757813292413,0.0323986388325866,-0.175072001125663,0.107930716799612,0.0475914999072129,0.342002974012503,1,0.96458222426258,0.619904015875891,0.209718705310238,0.383112320965967,0.287753902341824,0.0496005677577973,0.143987003565109,-0.0354893307283663,0.264190914452295,-0.402432046024789,0.0791761979778157,0.397201744853285,0.0116633912874361,0.259002554846793,0.464598070358448,0.359949359344132,0.334489041524036,0.233466732941818,0.231603691537437,-0.0573470108608444,0.066390972405214,0.0944970906317987,0.125216723578887,-0.115210751056038,-0.0390559541056582,-0.0801890797927928,-0.104964172205223,-0.0726982790318792,-0.034214533198523,0.0338452463956651,0.0571345786737108,0.00120724068240706,0.00058024929330386,-0.0178175251346989,0.0593110107648778,-0.0348509346006227,0.0836259749621856,-0.115483179421371,-0.00189598429295527,0.0583892335052586,-0.0358889741155561,0.0290465044803941,-0.0254954941311017,0.0294569468397649,0.0468075288203242,-0.0377540996470887,-0.0591364121734653,0.0199211914904079,0.075697334882421,-0.0836825831333498,-0.107882730036784,0.0895020579510977,-0.0679353572975915,0.0414804313566806,-0.123780367897584,-0.169990247756246,-0.0401742904325387,-0.0634066611582697,0.112595270754027,0.153470553847264,-0.0149152808593083,-0.127755485358632,-0.03509625125302,-0.0204953012923725,-0.0704956067929096,-0.133014390339852,-0.142990563078257,-0.0104393653855411,-0.0950241017834416,-0.141820795374608,0.00508575744285391,-0.00691997244709664,0.0521713715335351,-0.114917580004485,-0.0825305534450734,-0.140450283993041,-0.12238462314916,-0.635105693382232,0.537744197721457
## Hematocrit,0.0296532571162853,-0.0676184459812008,0.432506676617067,0.386837015962775,-0.0133593129001342,0.554897667522373,0.329248061122573,0.307426669340642,0.0534395455217346,-0.0999665699460659,0.0545805198286561,-0.176520564259761,0.105626884514558,0.0428992365354812,0.324986055161574,0.96458222426258,1,0.392548416738036,0.186836683486556,0.353897255166567,0.260058276022337,0.055895707976201,0.121694650597389,-0.0235989263955477,0.244561413045476,-0.37445621382715,0.0880427798463538,0.398114618737425,-0.00876486458697518,0.260964965681278,0.443882112174035,0.326051828952798,0.307850942772469,0.215666460433216,0.214024980075087,-0.0576122733252784,0.0703540809779519,0.104018422275666,0.117126061741312,-0.1282024720687,-0.0418586221394504,-0.0959224716092101,-0.117117501342164,-0.069746342534468,-0.0348707233690845,0.0669849002381249,0.0490139104404654,0.00321406873569511,-0.0119662564027594,-0.0276358130999827,0.0629868636007617,-0.0294832557200825,0.0662405642684997,-0.116603498302546,-0.00357939663927613,0.0946258201506309,-0.0221344100897666,0.0202503850660157,-0.0192391720895851,0.0345409414825878,0.0323152286917271,-0.033075880792378,-0.0463752823026234,0.0144220030884592,0.068041177219525,-0.104703228150057,-0.0931485642587916,0.101278044564534,-0.0756623267047219,0.0326658228542298,-0.137966169483497,-0.158434729210323,-0.0387591267692073,-0.070255211743446,0.0876282352156295,0.118995783264894,-0.00522890252147432,-0.119155218691794,-0.00960879496185386,-0.0208760101089507,-0.0533089327371406,-0.144013712610458,-0.12672820528242,0.00503796825216528,-0.0955291503375299,-0.126284806163011,-0.00664111562989089,-0.0332519770025051,0.0397999746493502,-0.0926209609559386,-0.0692853459589068,-0.128075377004168,-0.105212154777459,-0.603200180163915,0.484147722903868
## MCHC,-0.030498307993227,-0.0730995031678947,0.321941326326147,0.281530590566103,-0.00539492823815049,0.400053899064026,0.190075947076712,0.194509514734655,0.0466859008306633,-0.150067861876862,-0.0487450321577057,-0.089138771151224,0.0586197138584825,0.0315405466225083,0.225370511382947,0.619904015875891,0.392548416738036,1,0.1720386991699,0.27624324705837,0.228528914524238,0.0100840268684188,0.13789026664574,-0.051570160248834,0.186581262375537,-0.288472104435632,0.0134999047153028,0.201250544262996,0.0555524459599962,0.128373828980825,0.295055158715656,0.288628832800549,0.249616030266627,0.171086596209095,0.168325159517875,-0.0262725682072475,0.0200564213893228,0.020945921319818,0.0712463702535749,-0.033939153616209,-0.00505850244762723,-0.00718940666146796,-0.0308029438837574,-0.0502448262061002,-0.00897041173801115,-0.0747901990487953,0.04385477387756,-0.00386485839320742,0.0318301066829539,0.0128498950420707,0.0187928787018505,-0.0332767028083056,0.0928257421536204,-0.0544031534325691,0.00659356295997344,-0.0701126363983818,-0.0532280244142071,0.0369876377902088,-0.0315814478227109,0.00269028222372593,0.0665132301243871,-0.0403769358166675,-0.0642899468941428,0.0256236431682356,0.056846853442142,0.013845378547881,-0.0952285791230823,0.0156314910117222,-0.00150608313965005,0.0533487102818443,-0.0273501022587767,-0.111080702769312,-0.0214194914623079,-0.0148581906165529,0.117894709700012,0.180555711713452,-0.0378655752869231,-0.0841612248629031,-0.0887152056177452,-0.00787971079490874,-0.0934351604800104,-0.0298327638506231,-0.11733167921786,-0.0409041652736601,-0.0408126073541629,-0.109429163160048,0.0422758660996351,0.0777245894750881,0.0674618515529052,-0.130581056968397,-0.0718904842891018,-0.0986346478487858,-0.105890312547024,-0.414328185897121,0.422277012543843
## GOT AST,0.0068628531818738,0.0760176145727991,0.153078314146545,0.134133927085319,-0.00139580276918877,0.189580233317515,0.10170590910455,0.0528649940809604,0.0253244264169662,-0.191961467949873,-0.0874960696002911,-0.0444104736678964,0.0509710885662914,-0.0566324321493582,0.00583708920732223,0.209718705310238,0.186836683486556,0.1720386991699,1,0.660852450489819,0.186053537426989,0.515342228963962,0.318416941371008,0.0340906421114677,0.0948237205885311,-0.0500681859914473,0.041365372789787,0.0830876912046034,0.00512335657092376,0.0586541669365875,0.105640199029803,0.0646473864135784,0.194347672275705,0.128876117330188,0.156036406861946,-0.118893986033419,-0.061921366840885,-0.0410255103818049,0.021212366470726,0.0317861989043131,-0.0612227115894745,0.11223973568579,0.047667804732392,0.000274506389855077,-0.0619420922983623,-0.0735461940764761,0.0786860917281599,-0.0723931564754225,-0.0201577421278194,-0.0233758933370083,0.017640638486234,-0.0251187594707365,0.0450399712498338,-0.00531811611545912,-0.00926470905465882,-0.0705452049068321,-0.0577488675211231,0.0565395232861719,-0.0477684326744839,0.00611021184145976,-0.0318331946957458,0.00780448885749161,-0.0491709176307973,-0.0474898541661784,0.0723423274674747,-0.0585891413384309,-0.0105248770476118,0.0703209332578405,-0.00445226177543503,0.138238835972046,-0.0624459099283647,-0.0776696503677782,0.0205655090022326,-0.0864115233569267,0.016580539360704,0.0653552879236595,0.00267183936339494,0.0305469623044426,-0.0134531671363929,0.0787693110938571,-0.0162506413372299,-0.0567641179712897,-0.0560828098340107,-0.00081486570084009,-0.0321407669400017,-0.0937115969355736,0.0652059931007402,0.103459378598414,0.133521421453585,0.00827205504133224,-0.0745217450125637,-0.0887300673208662,-0.0573739464812142,-0.161797336417842,0.170503185660364
## GPT ALT,0.00227465656323271,0.105527932537722,0.270752883760424,0.402418627839598,0.19704472936774,0.390417390252658,0.367285319001965,0.330578767686959,0.188969834361624,-0.0896406677913927,-0.0589316018041604,-0.0519458088237887,0.25667341825048,0.0543724015620563,0.173075969238833,0.383112320965967,0.353897255166567,0.27624324705837,0.660852450489819,1,0.448403628184602,0.314845518104374,0.447339636553113,0.0180352469050681,0.292331090067757,-0.290118491433807,0.0970902751009566,0.146367660220228,0.0355552788010453,0.144795074692723,0.371342481525864,0.144662870401199,0.420894963948433,0.146820997635719,0.181778299292184,-0.0470499365195547,0.0609661451366087,0.0799129209389654,0.151363191565282,-0.0117106434329386,-0.0639676431483096,0.0226100395220025,0.00122414731216115,0.0333156571913215,-0.0639077664208216,-0.0780662338182315,0.0760798517323673,-0.00558893299848253,-0.0218870702517177,-0.0714493305360845,0.0593810044566502,-0.0472621330658822,0.119754501695756,0.0407899065497238,-0.0151042006945433,-0.0937530658339244,-0.0470475172050712,0.0882625768816383,-0.047800312626594,0.00959706866634065,-0.039495767832863,-0.0336765957962132,-0.0180578979899561,0.00426316353808041,0.134183804267157,-0.11554155185602,-0.0903306527396613,0.163868458030653,-0.0499891970968053,0.105877116003216,-0.140295621879869,-0.14586644023488,-0.0249051859276687,-0.120566593323434,0.00293987776760333,0.103663157906473,0.0386839061824233,-0.0546626963467371,-0.0197882905893614,0.0532248859303253,-0.0125164949463898,-0.0501162013606338,-0.177676903743082,0.0124106251048386,-0.0361564033975163,-0.14951441720999,-0.0211996845904619,0.118015510809735,0.186616810762576,-0.0146304528002563,-0.104435150093392,-0.156039531259622,-0.121128600005673,-0.329075309615122,0.343004608687763
## GGT,0.205157072208608,0.104850789299202,0.239055767848824,0.365634539154521,0.220519595766695,0.317951139343624,0.432310844576284,0.367080913990194,0.168310020170097,-0.0549683519325389,0.0125372693860629,0.00827509417417852,0.20573212118573,-0.0282196162913216,0.113081128090276,0.287753902341824,0.260058276022337,0.228528914524238,0.186053537426989,0.448403628184602,1,0.0975569669650163,0.238513117457457,0.139837399802356,0.291328714521256,-0.12532888446889,0.160845375692695,0.25207044524044,-0.177121912609255,0.169469963795346,0.396087580314646,0.0367589579354589,0.43539062448013,0.257843915685003,0.246592483113191,-0.0325129511083843,0.108193878018329,0.130171140477608,0.15446994081146,-0.00724510225786683,0.021028784745679,0.00255132801727552,0.0195002896291693,0.107649533012622,0.0208783680829128,-0.0786852891222483,0.00611345658185214,-0.10208413284574,-0.0551532877038911,-0.0414048440674157,0.0205760541491477,-0.0472249980275993,0.141760343487718,-0.00492656771431151,-0.0100003232159746,-0.00991166213568229,0.00607227614074714,0.0539395518469667,-0.0583513433879807,0.0147134491024157,-0.0540315936761698,-0.00573360768330186,0.126170310714669,-0.0339022881578179,0.244056307273326,-0.053814417143306,-0.0281478525762827,0.143329889254512,0.0229910155529617,0.0338545370361325,-0.0629763289344077,-0.137249579875286,-0.0149013610006469,-0.0359245073750856,-0.000962378353957512,0.08903434379838,-0.022410639400094,-0.0389488265036985,-0.0132176315122289,0.0336591985969847,-0.0159168120561121,-0.032978695560581,-0.0998036712667443,-0.0755548562408369,-0.0452849442790668,-0.0927156337464429,-0.0553256995826815,0.08620652035773,0.145593262837596,-0.0588813071677988,-0.07408958272715,-0.072024544960198,-0.0571234346315914,-0.331799950231292,0.251291820204052
## LDH,0.198845017852987,0.0985922976642754,-0.0463781214016796,0.0730021351702585,0.107763541961226,0.00701237698591976,0.11950088341001,0.0893413475946097,0.082175086314222,-0.123307230540619,-0.0205447167164689,0.0688537169031303,0.082603419856244,-0.0878744635128816,-0.131715721255636,0.0496005677577973,0.055895707976201,0.0100840268684188,0.515342228963962,0.314845518104374,0.0975569669650163,1,0.151991236452857,0.177230580347066,0.054564288999628,0.0857383459838451,0.123722448190866,0.0548961975044106,-0.2069794132844,0.176578209593369,0.00982321862182612,-0.0810700483680913,0.0980012515570259,0.164379019602029,0.152415008632008,-0.0660798803382536,-0.0484800072103675,-0.0315003821949534,-0.0574716498497314,-0.0267172701463403,-0.0360178622069674,-0.00815448474461855,-0.00878210129780493,-0.0278385105545687,-0.035648543145522,-0.0627975902574377,0.0245548288841013,0.0387769817117936,-0.00676862681412637,-0.0334433613017072,0.0770499923828076,0.0342713193837794,0.0543636842679892,0.0139755119071656,0.101877268398519,0.0278931031106583,-0.046129996131184,0.0958270347181943,-0.0457203723113728,-0.00237461688824391,-0.052001848975703,0.0725490919264608,0.00319231078964259,-0.108998550962578,0.0663849170924044,-0.0208342940507668,0.0116153268109463,0.0432287919051115,0.0142555224113736,0.0377567212175958,-0.0106306471514407,0.0116518631145044,0.0705343797963675,-0.0582165266371182,-0.00279167468893857,0.0445925011958266,-0.0338392351453415,0.0101459785787494,0.0451611765778173,0.0733725076541558,-0.121690911379916,-0.00959004926551564,0.0118875030626587,-0.027160197788405,0.0171394486201833,-0.0398377822660419,-0.00942236778042618,0.0812831006781524,0.0469584956727032,0.0508413913882128,-0.0121797063500422,0.0139273564353276,0.0145798691718731,0.0470065269484211,-0.00198542159376624
## Glucose,0.283680625149849,0.137720638612295,0.058948951956477,0.356205184473739,0.326856118021896,0.210489582663457,0.451388534221424,0.415467134093191,0.240221548032631,-0.0410214419662869,0.00683238328630066,0.0533881465818769,0.273696055288804,-0.00195688706595673,-0.00672745560050004,0.143987003565109,0.121694650597389,0.13789026664574,0.318416941371008,0.447339636553113,0.238513117457457,0.151991236452857,1,0.0834721914780941,0.375957748634725,-0.216713776557607,0.112415643783453,0.170346301137979,-0.230975809854364,0.172092336095554,0.236479316834914,-0.0389462109732735,0.40807245325655,0.2572256331975,0.23868795353892,0.0260667050148772,-0.0207713008571575,0.00145627717495795,0.0880984376634317,-0.00445551316398577,-0.00851616300591191,0.00938903716319499,0.0108071853104576,0.0515961323991998,-0.00897502055969748,-0.144729332069688,-0.0474805428757492,-0.0251853456246484,0.0379035571645929,-0.0154912906397354,0.188120332052566,-0.0331990171021632,0.0841100502680253,0.0416924875871558,0.00161538125013142,0.00923018555627217,0.0150031520082571,0.118145328120468,-0.0434402482876647,-0.040322448174285,-0.0191884286584214,0.021636786109416,0.0305287204800494,-0.104239392662693,0.101220417046555,-0.00257386400542428,-0.073371032843199,0.0241614606154911,-0.0362313923974112,0.0810114644697974,-0.0960048472731416,-0.124478949169652,-0.0131447093304259,-0.0540742975241487,-0.0199477349897807,0.0340898394233155,-0.0152576662454226,-0.013796640479297,-0.039448759980022,-0.037263347076892,0.0605758515146507,-0.0316175370657816,-0.12486771164734,-0.0702986715594967,-0.0133198257564181,-0.103749620237521,-0.0216164922938576,0.070825913898388,0.183651756877206,-0.00574623096565277,-0.0530636315341931,-0.0686904647943995,-0.0666017034129571,-0.196469941152273,0.184952763299143
## Cholesterol,0.419080711440776,0.0501717878975772,-0.278875541166133,-0.00042168585321633,0.244460144720276,-0.217147105617662,0.168273235082714,0.14345494803598,0.075997041641552,-0.189525944304483,-0.0777633853966827,-0.0483373545044591,0.0913930954064238,-0.0779355780526145,-0.174942636976375,-0.0354893307283663,-0.0235989263955477,-0.051570160248834,0.0340906421114677,0.0180352469050681,0.139837399802356,0.177230580347066,0.0834721914780941,1,0.30243885786819,0.29087368617307,0.890920510628977,-0.018233203077148,-0.404953953190834,0.187991632635429,0.0480150296339967,-0.106942950605879,0.0949551464438549,0.26999601475637,0.36107644174272,0.0649428552151202,-0.126492951971404,-0.121512115058899,-0.0883910110674879,-0.0377835464771965,-0.0140498389557723,-0.0746436975731615,-0.0255005251910606,-0.0260376808093493,-0.0156788720548184,-0.0461787627123197,0.0330062946075167,-0.0144631079303939,0.0166193005933014,-0.143025706813067,0.0394038859957899,-0.0640454224674897,0.139174264928357,0.103454769775095,0.0654474951039288,0.0184038874935068,0.0692745622996486,-0.00189434635574147,-0.0977339007210266,0.010612622597882,-0.0673093971214679,0.00636176449497903,0.0908889740807479,-0.140553231988422,0.0529258132664784,-0.0330109890044327,0.0648757238873713,0.0282756586482139,0.0390682920734421,0.0113308414911076,0.0456596499611281,-0.0779767114228106,0.162603437679461,-0.000438641726602725,-0.00860386161388619,-0.0343574804039513,-0.0192606627742362,-0.0184630752829613,0.0835248072306721,0.0293471205179208,0.0422664089254019,0.0379268830311074,0.0505199734018422,-0.0203569004979897,0.0406209127610543,-0.0325239938686947,-0.0403733275766421,-0.0334282851413789,0.0367286393405909,-0.00797297894980834,0.0211710710279287,0.0283111709768033,0.0202024939149536,0.166717879970144,-0.199284713230051
## Triglycerides,0.122066591678719,0.104546321034675,0.11658975283042,0.443673556422739,0.388698188723157,0.27854218238333,0.46604992124161,0.456260704543932,0.325447293309578,0.0162070973625027,0.205671672128691,-0.0268310314130251,0.390647845375906,0.0940964677924821,0.118541144405985,0.264190914452295,0.244561413045476,0.186581262375537,0.0948237205885311,0.292331090067757,0.291328714521256,0.054564288999628,0.375957748634725,0.30243885786819,1,-0.366629411098588,0.305861191388546,0.184160787133863,-0.134834900378333,0.0476203840537162,0.405200242330154,0.074929847660578,0.30811114141784,0.146233450245426,0.276487201131515,0.195654091660087,0.0207966227430493,0.051106088020693,0.146081095667534,-0.0499957981802214,-0.088715118938289,-0.0329149890384863,-0.0275021319773149,-0.00301877141147881,-0.0790105563624382,-0.117886206051906,0.0395517813085013,-0.0825350272914674,0.0506202745918653,-0.0499888996156664,0.0708444177232601,-0.0581120476117752,0.0726537310129818,-0.00689978546858691,-0.0294158493706253,0.113276584095732,0.0615743072242403,0.0436352319462745,-0.0108935667295029,-0.0202161302247615,-0.0109440335755535,-0.0592753575145957,0.0173328235708085,-0.08016535533931,0.0286119201691018,-0.117787198297991,-0.156673327252577,0.0500797886296386,-0.0706368836225593,-0.0456375540162408,-0.113135049305769,-0.344569561944785,-0.0134100823548716,0.0220241724584775,0.0118927833815653,0.142849228905952,-0.0679477078954009,-0.0854439075123554,-0.0889610433092474,-0.0151366072100621,0.0197952022679208,-0.0586263428713612,-0.143662151493243,-0.0517675656419915,-0.0292086586035565,-0.186707600977266,-0.0735956562461873,0.0954019215939902,0.180582130724839,-0.0362997485886526,-0.0611607589982681,-0.207076529986264,-0.151822573583164,-0.189041767983853,0.279381235248111
## HDL,0.0702688024352788,-0.000625052177099107,-0.430591425781593,-0.540837062678497,-0.233006993262197,-0.552867351970312,-0.403956203160037,-0.446734229916899,-0.268516281564376,-0.0123150765672222,-0.0754565104210603,0.0402452527079404,-0.208629880118111,-0.102521934893512,-0.306542592727523,-0.402432046024789,-0.37445621382715,-0.288472104435632,-0.0500681859914473,-0.290118491433807,-0.12532888446889,0.0857383459838451,-0.216713776557607,0.29087368617307,-0.366629411098588,1,-0.0607554165749509,-0.302492182204307,-0.0594830101223001,-0.0787200848691081,-0.479967151764222,-0.177584021270129,-0.290784032939709,-0.0546958166688468,-0.123328565593521,-0.00724442535487066,-0.107300398677937,-0.112838964502922,-0.158194498810135,0.067172232664175,0.0572989451047373,0.0268558056958454,0.0633510772697145,0.029458161218325,0.0460426652469698,0.0388254223856279,0.0498934970286851,0.0142440924944718,-0.0190569108392254,-0.0660648187084566,-0.0268094855940903,0.0350395298544452,-0.0475008045695922,0.0948260877582894,0.0447971282285663,-0.068555601436841,-0.0653027723675136,-0.0460413410044194,-0.0502695690546937,0.113325131202733,-0.0723097345781402,0.0188193382827854,0.0715563922380751,-0.0341192711487863,0.0421987337643754,-0.00271684782160009,0.22480814455743,-0.0421869240777535,0.00288326686651591,0.00599887210231593,0.142839698581006,0.114150147047299,0.0909159450216549,0.063663412969325,-0.038514963244705,-0.0851831556847826,0.0338438031053921,0.12702197441401,0.0254718441412762,-0.0395691710606982,-0.0610417307462024,0.128234103824436,0.170923939989618,0.0265244534290438,-0.024308103514758,0.0928533921630947,0.0891150557952695,-0.056029653632464,-0.0988295076031066,0.0314792101358152,0.0535546717935757,0.162061817611649,0.146612798733963,0.475009319647746,-0.490248685934803
## LDL,0.384316792093568,0.0184188989312026,-0.13993889872077,0.17755440232586,0.329839061167443,-0.042923086856529,0.304504624618962,0.298626520517979,0.17512696970141,-0.176653148000709,-0.0346144934136852,-0.0465972151685315,0.148209685732453,-0.0442588489686528,-0.0789336791051191,0.0791761979778157,0.0880427798463538,0.0134999047153028,0.041365372789787,0.0970902751009566,0.160845375692695,0.123722448190866,0.112415643783453,0.890920510628977,0.305861191388546,-0.0607554165749509,1,0.0618527647649593,-0.370645546259757,0.18769106989312,0.206543855828154,-0.0282019805841072,0.165420316585345,0.274030405828801,0.392334356026787,0.057520613819776,-0.107598488817792,-0.117167610363774,-0.0527087731851008,-0.0599076049934921,-0.0474108178969916,-0.0814095625416831,-0.0505827825423601,-0.0415757679558237,-0.0449699750276632,-0.0274886548031592,0.0329313497424852,-0.025815642458227,0.0336043472142131,-0.101334807831991,0.0187117666979188,-0.0635013660271302,0.13356993143011,0.0669873335089156,0.0261999164780403,0.0438303987269542,0.127402434875792,0.00193621855382142,-0.0826714931073854,-0.0294035567003595,-0.049751382235939,0.0273770589347461,0.0637009261735065,-0.12008157516197,0.0380907255310725,-0.014879222944262,0.00449800948190389,0.0394809033311808,0.0340359504924025,0.0113821902234977,0.0238756387644231,-0.0749226714141812,0.135671402712505,-0.0424864650241679,-0.00369467521849268,-0.0287529346108697,-0.05637792021492,-0.0650770039402848,0.0931817348009988,0.0577448592738027,0.0675331430841561,-0.00853792677245702,-0.00975728834247895,-0.0153637491499817,0.0660822593792879,-0.0607079772761177,-0.0859389654135322,-0.0361110176755336,0.041785015769476,-0.015926134229815,-0.0188072973222807,-0.017195198498842,-0.0344373463685929,0.0285415758629075,-0.0384655778262741
## Creatinine,0.0764022604319091,0.000162985858482369,0.382096901504131,0.319150795191466,-0.0710381521311265,0.510972285721626,0.275251626086776,0.221778530263176,-0.0143881086448218,-0.115123400084088,-0.101680660338221,-0.122766853380673,0.0961416290313474,0.0726455550411794,0.206258316757017,0.397201744853285,0.398114618737425,0.201250544262996,0.0830876912046034,0.146367660220228,0.25207044524044,0.0548961975044106,0.170346301137979,-0.018233203077148,0.184160787133863,-0.302492182204307,0.0618527647649593,1,-0.491015932208199,0.455249442376044,0.48010394683251,0.116314707224633,0.32035962944643,0.186470167280753,0.109372184200168,-0.16687866932031,0.0333411837144256,0.108643314165199,0.0874849836685089,0.0108726786516795,0.00784502563217193,0.0126743778636937,0.028676791057852,0.047266725167765,0.0155471112214597,-0.0560488374875783,0.0400029895734018,-0.0825233118866766,0.0468532128169261,-0.041898913969146,0.0670921798645953,0.0223346565454995,0.114155511531252,0.0167655174693113,0.0107331159482352,-0.0711137993339065,0.0253510146967173,0.144115299666238,-2.05603591808152e-06,0.0349894871522953,0.0677746039348277,0.0384924525646207,-0.0677279428886721,-0.0652949350970155,0.036662530245693,-0.00815450156698027,-0.0677972648866265,0.0245729098178181,-0.0829882739878727,0.0240485605954592,0.00969864305631893,-0.115669739569441,-0.0393984121726508,0.00410584119496658,0.0384366636797137,0.0837137450567922,-0.0656168969077718,-0.104167588717396,-0.0228048794244805,0.0319288925031854,-0.00134088740990384,-0.101085129347092,-0.117328249316393,-0.0554221358331169,0.0399346706460126,-0.15257247026992,0.0171329611983413,0.0554690109942724,-0.0536736964130929,-0.0538577963239445,-0.0459279374295939,-0.0659600044062179,-0.0646491039979221,-0.574934136282446,0.333889438518959
## GFR,-0.773223135423936,-0.0972552098142298,0.213738870534483,-0.134028788452365,-0.326542815999053,0.101167237829264,-0.357849640102507,-0.309020074507521,-0.142163982391671,0.222662764474371,0.0384774893271003,-0.063296402481825,-0.198515202690798,0.0279604371480137,0.268909154203561,0.0116633912874361,-0.00876486458697518,0.0555524459599962,0.00512335657092376,0.0355552788010453,-0.177121912609255,-0.2069794132844,-0.230975809854364,-0.404953953190834,-0.134834900378333,-0.0594830101223001,-0.370645546259757,-0.491015932208199,1,-0.453702944842623,-0.227637504823073,0.13710128143236,-0.287310218624754,-0.378773185391379,-0.273772847222063,0.0810897083622416,0.0685485025792278,0.128530634234253,0.115283445830296,0.0231816448291987,-0.0512089638997241,0.0573809483810506,-0.00970669370525245,-0.0369571935006658,-0.0532329032986255,0.138576828896324,0.0181385418048168,0.0139410794522463,-0.000791932154089913,0.163912123931285,-0.09158816551767,-0.0383541945160772,-0.136632541425348,-0.0533062926142222,-0.106056353574617,-0.0511242575880154,-0.0411945218202545,-0.121811786339377,0.0618652054937301,0.00609352471695674,-0.0375657227836531,-0.0848988103495656,-0.0717720751777979,0.164164158774677,-0.128816836968152,-0.0380635193659427,-0.0531393763041733,0.0414204520959934,0.00554485990033197,0.0676054451013365,-0.0996079081139005,0.0389505239530838,-0.0101605287887041,-0.0832306691051918,0.0157573289204928,0.0326331358665673,0.0357748261415548,-0.0260603847908034,-0.00951702307194652,-0.0225744440791718,-0.00324378015337884,0.0288455020210714,-0.094588648071942,0.0166995542203283,-0.108878432231042,0.00527550544718023,0.0387341531591934,-0.122213838994105,0.100758203450602,-0.0449717999232484,-0.0483894342115421,-0.0997449391821805,-0.0803293996128726,-0.0169711653652572,0.202937380713264
## Urea,0.398944975516159,0.0122565910869697,0.0707031777731027,0.175678578637618,0.0887884749897682,0.167983903977035,0.251965680728531,0.219069342120492,0.026597106397664,-0.241720923510282,-0.123062770017209,-0.0466691600208207,0.133078568656842,0.0346477067786679,0.00874079275017333,0.259002554846793,0.260964965681278,0.128373828980825,0.0586541669365875,0.144795074692723,0.169469963795346,0.176578209593369,0.172092336095554,0.187991632635429,0.0476203840537162,-0.0787200848691081,0.18769106989312,0.455249442376044,-0.453702944842623,1,0.348385220015262,-0.0378059038623358,0.345131072254929,0.331261333430357,0.197545990745597,-0.184385458210672,0.0564813811217515,0.0391935427035548,0.0740009904984969,-0.0507894379117579,-0.040876927734166,-0.0447067536999683,-0.0398098461574422,-0.0218438033808979,-0.0378895575425862,-0.0173153515801966,-0.0867800615643949,0.105137772808202,-0.0175233412119596,-0.130931509233315,0.154329645625585,-0.0632885001826062,0.164425055704716,0.0366554987904966,0.0630155679806626,-0.0237773141268085,0.0195904235424731,0.145761022946561,0.00391809380366744,-0.0164566118623844,0.00436813904650105,0.017583967636327,-0.0446631861802163,-0.0413628378270737,0.0160875424491343,0.0997105878068796,-0.0617063870081659,0.0398797093530037,-0.0452650668943625,-0.0730002828324652,0.0189147161033617,-0.0482308734892695,-0.0257929300104938,0.0676934240256055,0.0206458429250284,0.0205751447437593,-0.0662524900385389,-0.0691045458923854,0.0129108410206683,-0.0390981718152012,-0.0223124140182722,-0.00661942986614939,-0.046597124126416,-0.0628162513539249,0.0448721868646204,-0.0499711679743285,-0.038509355194571,0.0898647953055508,-0.00281776749880743,0.0295684764588664,0.0231767947311235,0.0106122283470918,-0.0228635067715788,-0.281534893704587,0.0985014985110573
## Uric Acid,0.228591516852409,0.0452266009164798,0.380521819790287,0.571155796893899,0.288061828591242,0.546646462619201,0.603446617682579,0.563208620235801,0.284939242935086,-0.0373001497763412,0.101120616609972,-0.0196261332465414,0.3314108521545,0.0418019138087151,0.217885667090335,0.464598070358448,0.443882112174035,0.295055158715656,0.105640199029803,0.371342481525864,0.396087580314646,0.00982321862182612,0.236479316834914,0.0480150296339967,0.405200242330154,-0.479967151764222,0.206543855828154,0.48010394683251,-0.227637504823073,0.348385220015262,1,0.166211381802068,0.536384434015752,0.303431006041749,0.237311816686464,-0.0137310131668321,0.126439135534737,0.0988925581044786,0.18379629667609,-0.0649004184927556,-0.0782596736317573,-0.0223044240624103,-0.0411524236677019,0.0177336178704165,-0.073545095516008,0.00865262299428501,0.0730127800044649,-0.0358414339903211,0.0146817214993287,-0.0300266398606546,0.0205868676238758,-0.053452382614813,0.12092556509957,-0.047695210797113,-0.0254706817810153,0.0688757764050613,0.0639280986652212,0.117866165274551,-0.0356436591355121,-0.0174695428004384,0.0828080297580775,0.066491369390465,0.00377754472222634,-0.0229114283284145,0.119774258898723,-0.0526734822794567,-0.166334935883862,0.0620328123996399,-0.0837079101705363,-0.0326224359751755,-0.0819105383665468,-0.229681325487075,-0.031444549403965,0.0202893568073173,0.0594691487835479,0.156748347656788,-0.0481044678605319,-0.186333218709354,-0.107060519003791,-0.0256799903925681,-0.00743290881156664,-0.0826121745308028,-0.192099140959646,-0.0883500187570228,0.0159576777743425,-0.221173500302759,-0.0333973668930977,-0.000417778152799829,0.0523930006430508,-0.0345743462856489,-0.120017772442134,-0.169328592329173,-0.151200176346972,-0.575148541072422,0.470830559542396
## Iron,-0.195736899877867,-0.073643433446511,0.193451760892118,0.0623255500110475,-0.114219599369008,0.188719229315117,-0.0168489361615362,-0.0112629664497649,-0.0674341532605858,-0.024647723099651,0.0372267935902959,-0.167754236608827,-0.033246299443423,0.0908687922066465,0.282237884922674,0.359949359344132,0.326051828952798,0.288628832800549,0.0646473864135784,0.144662870401199,0.0367589579354589,-0.0810700483680913,-0.0389462109732735,-0.106942950605879,0.074929847660578,-0.177584021270129,-0.0282019805841072,0.116314707224633,0.13710128143236,-0.0378059038623358,0.166211381802068,1,0.0770012251014169,-0.0314546869810673,-0.0476041660510878,-0.0769100816851891,-0.00257403676617434,0.0135273112970876,0.054639148863137,0.0512001547811404,0.0440496801920618,0.0878045054962254,0.059967846990109,0.0199616989503199,0.0462320228421641,-0.0278410977246199,0.0992002223395458,-0.0409035540678477,-0.0410020570334912,0.0628312410604012,-0.0168520550937321,0.0419096853706137,0.0452068217956464,-0.0267795140443908,-0.0676276407658137,-0.00711999350404063,0.0393121873092484,0.0173696255331177,0.0979400662441807,0.0508746985063094,-0.0176247303661756,-0.0573863178336671,-0.030237551393914,0.0555552691343371,0.0213577602671872,-0.00614439441194974,-0.0500019287570581,0.103535567395642,0.00615485505754465,0.00274574484299108,-0.00150704839669666,-0.0170122895136825,0.0418040962715831,-0.0961695088202763,-0.00606836476042863,0.0668529056597439,-0.0694838626204395,-0.0165800847286485,-0.00452022863319777,0.000767366645644657,0.00326355623799906,-0.0530393382755023,-0.055910809303695,0.0160743419698159,-0.0737534280375419,-0.0454602079527184,0.0667246946358373,-0.0406283733554546,-0.00167547077737046,-0.0781438735307493,0.00889382322513383,-0.0279966841027492,-0.010493529416907,-0.193503815039119,0.20402472872281
## Ferritin,0.359416365464615,0.105447362933263,0.233428241008525,0.446512304989,0.297020189486699,0.363742127300706,0.573585993835659,0.496579015124054,0.232125759508358,-0.157918580140953,0.00813845581016593,0.0212590291999719,0.338944069053123,0.040774841449757,0.0860073000149713,0.334489041524036,0.307850942772469,0.249616030266627,0.194347672275705,0.420894963948433,0.43539062448013,0.0980012515570259,0.40807245325655,0.0949551464438549,0.30811114141784,-0.290784032939709,0.165420316585345,0.32035962944643,-0.287310218624754,0.345131072254929,0.536384434015752,0.0770012251014169,1,0.310870984121955,0.230652399399448,-0.0453676817018114,0.0873674336681026,0.052121960406578,0.0903383674094956,-0.0670352003250332,0.00882402099745975,-0.05490978931469,-0.0518659298511264,0.0456896725563386,0.00881016740940184,-0.00622595709254898,-0.00992910966101406,-0.0683190904434736,-0.0997270406141221,-0.114379317853359,0.109616194210513,-0.047733910313002,0.115262310011179,-0.068290891720132,-0.00556142966951823,0.0588524393692868,-0.0141978486348928,0.117973597581931,-0.0114368600513705,-0.0020296370013413,0.0339759774905633,0.0618703143885805,-0.0102293224931797,-0.132652512449232,0.158824061877315,0.0247277730811069,-0.148297939420811,0.131794114149479,-0.0860106814803007,-0.0358919145330233,-0.145168845029679,-0.108390129006834,-0.047631213013542,-0.0698148930986251,0.107242818863509,-0.0517589041213755,-0.0412978825928046,-0.062706365283512,-0.111224330523616,0.0130095984416819,0.0722349588904449,-0.0459295007716909,-0.120957424832532,-0.0914575231401548,-0.0192334132725823,-0.1081066329239,-0.0359937097810155,0.14726580700891,0.045006101944683,-0.105664711563957,-0.0995807562906505,-0.104116652434683,-0.0968374368525472,-0.419672245014789,0.281021639874914
## BP Systolic,0.543066770941934,-0.0933911473989838,0.0486775354520486,0.278747046641116,0.245104236550589,0.174194380042852,0.398179032579535,0.394910534103513,0.168590615350702,-0.106143985799144,-0.0651683032121103,0.00515116226183895,0.120863054528532,-0.0357541415689929,0.0546114033240796,0.233466732941818,0.215666460433216,0.171086596209095,0.128876117330188,0.146820997635719,0.257843915685003,0.164379019602029,0.2572256331975,0.26999601475637,0.146233450245426,-0.0546958166688468,0.274030405828801,0.186470167280753,-0.378773185391379,0.331261333430357,0.303431006041749,-0.0314546869810673,0.310870984121955,1,0.767183269297492,-0.0876379264032171,-0.0207291559653088,-0.0628779642000323,0.0107629508905034,-0.0229556872676035,-0.0301104114728042,-0.0188134098089573,0.00416729326692879,-0.00432046732942366,-0.0320081885168539,-0.0885690844862161,0.0283770027998442,0.000608729455317064,-0.0219049488839337,-0.0813590464000212,0.114149009768994,-0.0235271700432031,0.177568891620045,-0.0509663712067597,0.147812949777093,0.073547481198908,0.0102252107665833,0.0308246175870277,-0.0574645682429839,-0.0243269428436678,0.0330737649796942,0.0398488414674901,0.133254227607593,-0.112319198483499,0.165129333036763,0.0293003996764932,-0.0910408843344971,0.00830630183205247,0.0210792218860463,0.0185044955514897,-0.00499328684769282,-0.050526582842067,-0.00968039160465129,0.00489755202296758,0.0189566599385693,-0.0476107067910089,0.00995506084548149,0.0170546491955391,-0.0453542902576893,0.0179629914599309,-0.0350954059931169,0.0414403978718254,0.0673041149177563,-0.0911482468160587,0.0219826802441747,-0.0195420365861132,-0.0946903773058388,0.0633536126387731,-0.0401795904858022,-0.00876355371977187,-0.0412604289209078,0.0694818336890962,0.0682373189412681,-0.295960513167008,0.198632162742518
## BP Diastolic,0.37882448087062,-0.0400749754068231,0.0483587203823246,0.380423835836508,0.39517586561208,0.184007606215157,0.395924035666075,0.447439651380319,0.33481216012119,-0.112979356849165,-0.0420406472048182,0.00479461471942885,0.181088102818473,-0.0539093700683251,0.0852420865987778,0.231603691537437,0.214024980075087,0.168325159517875,0.156036406861946,0.181778299292184,0.246592483113191,0.152415008632008,0.23868795353892,0.36107644174272,0.276487201131515,-0.123328565593521,0.392334356026787,0.109372184200168,-0.273772847222063,0.197545990745597,0.237311816686464,-0.0476041660510878,0.230652399399448,0.767183269297492,1,0.118032657018989,-0.047092086435316,-0.0458785151135567,0.0130591227944465,-0.0424539316314173,-0.0344935475724951,-0.0343930572921367,-0.0195463928204421,-0.0253199734275282,-0.031850724910783,-0.0815760730584102,0.0592488272898921,-0.0196355815072212,-0.023555498558526,-0.0177809137545296,0.0995800987603306,-0.000230426786610934,0.191266331197157,-0.0157494869032926,0.097849102707864,0.0602072224447626,0.0259794068974945,0.0202907613661736,-0.04203386873122,0.014437558437645,0.0550392520471051,0.0638380443036153,0.0690636537374766,-0.107994294485042,0.0484952031894661,0.0284524511691361,-0.127470586759038,-0.00780870787874527,0.0496617278070936,0.026263857426599,-0.0469776745041724,-0.106208775479952,0.0609173422458371,-0.0121695697598753,0.0164003997441294,0.00830904562520199,0.0147492319651185,-0.0341836950836401,-0.0513879236458354,0.0551355316256867,-0.042402804481282,-0.033353370620603,0.0176165745234091,-0.0506705548465069,0.0360277503611793,-0.0405703867809975,-0.104413321490275,0.0248412139723888,-0.0046753608563755,-0.0226965148964878,-0.00469743894886972,0.0243997116770987,0.0424957408373283,-0.165223698481579,0.246604577397413
## Heart Rate,-0.0421958205140314,0.00862288563940877,-0.104647072844746,0.039406685485827,0.169250570491403,-0.0946329568639018,0.0650285221188822,0.0722903484495167,0.138709161762108,0.236991085734166,0.199575649072421,0.126795328373915,0.122902819791154,0.000898143516818937,0.071213077266803,-0.0573470108608444,-0.0576122733252784,-0.0262725682072475,-0.118893986033419,-0.0470499365195547,-0.0325129511083843,-0.0660798803382536,0.0260667050148772,0.0649428552151202,0.195654091660087,-0.00724442535487066,0.057520613819776,-0.16687866932031,0.0810897083622416,-0.184385458210672,-0.0137310131668321,-0.0769100816851891,-0.0453676817018114,-0.0876379264032171,0.118032657018989,1,0.0474960328610823,0.0968067235593637,0.0605411943212255,-0.0202629903548005,-0.032699900462053,-0.0010910031729893,-0.0165253584079164,0.00735359415156043,-0.0325119688082755,0.0289320285804609,0.037078526623695,-0.0743859201401929,0.119859664551344,0.042201849736092,0.0306224838323836,-0.0401001681342616,-0.0524545918632084,0.00476670372259779,0.0304798019342067,0.0752643826568258,0.0127001537491171,0.0511379955318169,-0.0375666431844286,0.023334838584519,0.0427789532295942,0.104456741316354,0.0159414887827104,0.106942442835073,-0.0227068670851758,0.0202108288526635,-0.0638341410473809,-0.13522265436203,-0.0435081565085511,-0.0632749499518925,-0.0487958005953125,-0.0965580286002473,0.025681348310982,0.109972043451246,-0.0246255396081241,0.10452824046852,0.0212409578095193,-0.0845740173862706,-0.0319555720404804,-0.0814618059141526,-0.0489495802797117,0.0639454627617467,-0.0987462171562396,-0.0259416204352749,-0.0894407887513698,-0.104620686343199,0.00145566730604256,-0.0663156958141818,-0.0603579346241633,-0.0847834198677987,-0.0976678740756682,-0.115500677906575,-0.0762838743253361,0.15778652581411,0.0353312768770485
## acetic acid a,-0.0395957799425808,0.0349184585280418,0.0150336661537965,0.0910620437868223,-0.00621392164138514,0.133367305864791,0.069138194130598,0.101671289952802,0.052000867405524,0.109664809415007,0.0524385076693959,-0.0146035016671296,0.0225453232869625,0.00317722621842317,0.155135955815847,0.066390972405214,0.0703540809779519,0.0200564213893228,-0.061921366840885,0.0609661451366087,0.108193878018329,-0.0484800072103675,-0.0207713008571575,-0.126492951971404,0.0207966227430493,-0.107300398677937,-0.107598488817792,0.0333411837144256,0.0685485025792278,0.0564813811217515,0.126439135534737,-0.00257403676617434,0.0873674336681026,-0.0207291559653088,-0.047092086435316,0.0474960328610823,1,0.701075759977428,0.651281545251859,0.047251893596638,0.257835745996942,0.168821701894854,0.047717311506476,0.372487212400147,0.258844130769221,0.303760025863441,-0.00432717006183959,-0.0517076953903179,0.0217272070478794,0.0610515898772581,0.182090474458787,-0.0726423146652533,-0.0105701344679019,-0.12153771836698,-0.00299694905856846,0.0431170535387316,-0.0545615302410078,-0.0223734766348664,-0.0836307170302387,-0.0244839756307652,0.188775804566274,0.0382413056896984,-0.049932094742365,0.214796353845826,0.0399120492139041,0.0776302366560881,-0.0946062939195782,-0.0194764503080092,-0.0467721145817746,0.0552519560524483,-0.119445843262432,0.00581713849027584,-0.0029425695283737,0.0303014774087439,-0.062306008438864,0.000114201284068335,-0.0907792075359173,-0.177371829213373,-0.0423231006562109,0.0747378667294589,-0.0204483906221738,-0.0250177726411095,-0.109387915380571,0.0107370587464708,-0.0554162144938745,-0.0544801777993989,-0.010691789303417,-0.0361175265521343,-0.0217523743320743,-0.142339511040283,-0.058559953851604,-0.0928706082944952,-0.108889084391714,-0.132587500627366,0.0744242411147501
## butyric acid a,-0.135369553886164,-0.0692506079782795,0.12389382527992,0.0930560484811709,-0.0654708551713756,0.188659174439262,0.0368509190235835,0.058602352464058,0.0125610801939082,0.142608082448957,0.0414754844781804,-0.0140640664965929,0.05884716101483,0.000844744473399949,0.180273810308132,0.0944970906317987,0.104018422275666,0.020945921319818,-0.0410255103818049,0.0799129209389654,0.130171140477608,-0.0315003821949534,0.00145627717495795,-0.121512115058899,0.051106088020693,-0.112838964502922,-0.117167610363774,0.108643314165199,0.128530634234253,0.0391935427035548,0.0988925581044786,0.0135273112970876,0.052121960406578,-0.0628779642000323,-0.0458785151135567,0.0968067235593637,0.701075759977428,1,0.652689212514227,0.192397305160295,0.33350516619188,0.232060074722321,0.186420837478759,0.542608551625729,0.339488013906567,0.211359711094845,0.0115443199876583,-0.0636529702756079,0.0201429974599525,0.0274009015195898,0.199137967634094,-0.0664645343804104,-0.0219670026268523,-0.0710024756048229,0.0105472563513753,0.00513766780950441,-0.0180931007586852,-0.0173336726286135,-0.0912181667611517,-0.0216740207122904,0.259920906180064,-0.0440610216978754,-0.122467642791351,0.228221135550696,-0.00366684929210747,0.040607921321475,-0.115480542912606,-0.0339866330572611,-0.0688519406558985,0.0263257254125686,-0.184821773613198,0.00113190340705889,-0.0393495650822929,0.0141757834648739,-0.0275417652443211,-0.00111229714751792,-0.0596025967207811,-0.224185195921025,0.0565558568378281,0.0913859141482798,-0.0117679576100281,-0.0496173657505923,-0.195980573974911,-0.0189759903009309,-0.0469156622334224,-0.126530954297898,0.00212766047839817,-0.0811452373910057,0.015647922418825,-0.153184947737229,-0.0789017245698165,-0.128079002438291,-0.138986129926731,-0.196469238392555,0.120078933472747
## propionic acid a,-0.093233876745631,0.0127264695258399,0.0953695623264191,0.192191180670079,0.0420300962760202,0.232597577704909,0.161575182731451,0.197079811857077,0.0903219662255707,0.145994204479597,0.0596214765427855,-0.0228437908477702,0.134542580050459,-0.0200966895907134,0.17115496797889,0.125216723578887,0.117126061741312,0.0712463702535749,0.021212366470726,0.151363191565282,0.15446994081146,-0.0574716498497314,0.0880984376634317,-0.0883910110674879,0.146081095667534,-0.158194498810135,-0.0527087731851008,0.0874849836685089,0.115283445830296,0.0740009904984969,0.18379629667609,0.054639148863137,0.0903383674094956,0.0107629508905034,0.0130591227944465,0.0605411943212255,0.651281545251859,0.652689212514227,1,0.256054776149027,0.0984339805182646,0.363487304826864,0.253722983689357,0.481633118552646,0.103294955703103,0.14993390625061,0.124380424216554,-0.0844039575898375,0.182970904353181,-0.0308967188311683,0.0833517526682858,-0.064561116071679,0.0265024245395366,-0.10799651148106,-0.0310295631385593,0.0358958907611845,-0.0665569250689678,0.0415419665075118,-0.129255762326176,0.0250463463115173,0.16123138886205,0.0190744605314114,-0.215224533076869,0.068148527853652,-0.0527939982099953,-0.0643621151825613,-0.17859725057638,0.0844437044568629,-0.103659547731911,-0.00943168308069092,-0.236284342129272,-0.315016180054705,-0.016424003816159,0.0642513166976426,-0.0387760083796206,0.102526462114511,-0.110328055616135,-0.35263858336186,-0.0790394328050164,0.0602435984924073,0.0130605111959126,-0.0868454753216309,-0.388429481011648,-0.128009570834082,-0.0585757630006605,-0.347321714371023,-0.027632136193234,-0.0881395628091863,0.0915907567034642,-0.153636527522735,-0.131213206819088,-0.360147428821021,-0.345626096030621,-0.21733499780524,0.186904720241133
## 2-Methylbutyrate a,-0.0482196553660839,-0.030596251056701,-0.0411071805097411,-0.0216145526750559,-0.0180582545486415,-0.0143262878503184,-0.0253642635663647,-2.49381498907089e-05,-0.00343024980709604,0.0653214431313893,-0.057536348971791,-0.0189867506304218,0.0346753746219812,-0.0203614476286757,-0.0846176714775511,-0.115210751056038,-0.1282024720687,-0.033939153616209,0.0317861989043131,-0.0117106434329386,-0.00724510225786683,-0.0267172701463403,-0.00445551316398577,-0.0377835464771965,-0.0499957981802214,0.067172232664175,-0.0599076049934921,0.0108726786516795,0.0231816448291987,-0.0507894379117579,-0.0649004184927556,0.0512001547811404,-0.0670352003250332,-0.0229556872676035,-0.0424539316314173,-0.0202629903548005,0.047251893596638,0.192397305160295,0.256054776149027,1,0.31323437619881,0.903367499024703,0.986666036106476,0.668207515867263,0.311223609391434,-0.101083400803668,0.116471420742594,0.0138088586155741,-0.147747840843862,0.00543213988386957,-0.0327269690761865,0.045842672577157,0.147490200063145,0.108523161666898,-0.0204807755456346,-0.0182416853815034,-0.00418538833203675,-0.0615001613011639,-0.0627362773962034,0.00842211736616918,-0.135386423209351,-0.0287156200666522,0.241405024480733,-0.203758546295235,0.167920695950932,0.0494484733370976,0.169418456038392,0.0128164988522683,0.11029266429893,-0.00300737143585304,0.166318247780809,0.157729151398393,0.0554547205854018,-0.0188657094873322,0.0669117265518229,-0.0753437374892097,-0.0621869140783974,0.130326021158363,0.0606581772993886,0.21095891011596,0.0361362268174009,0.0639771355551443,0.173364151252765,-0.0163543613465746,0.0705083789505147,0.0932717844771715,0.0889227236560874,-0.0340126203305344,-0.0821070260038158,0.145356206217962,0.0830418958881578,0.133424616746606,0.114632486456763,0.0090013873618995,-0.00495229763388459
## hexanoic acid c,0.0540636063973095,-0.0179228125013649,0.0163121655077653,-0.0225043056104213,-0.0433906040582158,0.00683706269378284,-0.011104502814807,-0.0193256371589784,-0.0339647782128689,-0.0460103689172076,-0.0302142299323346,-0.0215133490120414,-0.0189004999367869,-0.00767519038396478,-0.0477077213488395,-0.0390559541056582,-0.0418586221394504,-0.00505850244762723,-0.0612227115894745,-0.0639676431483096,0.021028784745679,-0.0360178622069674,-0.00851616300591191,-0.0140498389557723,-0.088715118938289,0.0572989451047373,-0.0474108178969916,0.00784502563217193,-0.0512089638997241,-0.040876927734166,-0.0782596736317573,0.0440496801920618,0.00882402099745975,-0.0301104114728042,-0.0344935475724951,-0.032699900462053,0.257835745996942,0.33350516619188,0.0984339805182646,0.31323437619881,1,0.250390146727675,0.308492687798735,0.654379238148439,0.997007794969872,-0.00274579012107999,-0.0171135081659378,0.0312725071375869,-0.137573550696034,0.0393353488684622,0.180009260193911,-0.0185717095701943,0.0410792959149305,-0.0897140792764021,-0.0214915460398337,0.0306968835611316,0.0581556421580576,-0.0425932976374511,-0.0251385870040158,-0.045106499997691,0.0532851568755651,0.0101582449998658,0.0653088518308629,-0.0512705117374176,0.118626131108109,0.0724980350662342,0.0594974614922792,-0.0712846607613222,0.00564708348425256,0.00966595850521988,0.0451179579351857,0.223191046128354,0.0322168596323364,-0.0394587067242015,-0.0396105965646251,-0.0841263205359281,-0.0392974540950212,0.000738446793285618,-0.0180452943898788,0.0750438494806153,-0.0263954774217103,-0.0450271911055889,0.165219779847449,0.0649735198444059,-0.0470209902422969,0.220527584798625,0.0556185487905652,0.012747552626375,-0.0956706646350466,-0.0254012245484089,0.115459964764221,0.219332794762261,0.198723467920976,-0.0179829185251035,-0.0389393261105942
## Isobutyrate a,-0.0778733189869173,-0.0570555908215686,-0.0330228951253012,0.00337946968814554,-0.00563722619364213,0.00975431527903456,-0.0229200231701553,0.00197625668272699,0.0240050688106408,0.07335035204823,-0.0440981878088322,-0.0183127463888408,0.0304525860125473,-0.0390605268073839,-0.0367348359276858,-0.0801890797927928,-0.0959224716092101,-0.00718940666146796,0.11223973568579,0.0226100395220025,0.00255132801727552,-0.00815448474461855,0.00938903716319499,-0.0746436975731615,-0.0329149890384863,0.0268558056958454,-0.0814095625416831,0.0126743778636937,0.0573809483810506,-0.0447067536999683,-0.0223044240624103,0.0878045054962254,-0.05490978931469,-0.0188134098089573,-0.0343930572921367,-0.0010910031729893,0.168821701894854,0.232060074722321,0.363487304826864,0.903367499024703,0.250390146727675,1,0.900940502740108,0.598504558535772,0.247640983637422,-0.0175283195539343,0.162831490052914,-0.00574539123183125,-0.118503685898067,0.0208888869626697,-0.0119161811028567,0.0141955071812069,0.128554038915144,0.102593138714241,-0.00941797483151129,-0.00813019912148073,-0.0201586266253029,-0.0392764511052362,-0.0764656961773818,0.0329969280675953,-0.154640108352854,-0.00977417081956441,0.190642141022178,-0.185504172280991,0.137742588739202,0.0966540570278123,0.156532570837988,0.034816058701913,0.0859589628587081,0.00987016693568436,0.153874848186673,0.130022284232798,0.0418744747775243,-0.0224998427039497,0.0430593899619187,-0.0461589878414422,-0.0523504532507892,0.103122795861221,0.0318050011297583,0.18197244522596,0.0266392456145783,0.0529958942215383,0.134984749602082,-0.0263138108490669,0.0410294296739098,0.0708667704890086,0.0744831005309429,-0.0404803511226347,-0.0633001946089275,0.117584969156899,0.0469425045033971,0.0942636399139544,0.0780938481855311,-0.00483032194204923,0.0220669639700323
## Isovalerate a,-0.0143129327619469,-0.0311441641724398,-0.0398351926308116,-0.00300641087081474,9.61623715814834e-05,-0.00428773589154429,0.00270142313887912,0.0229053019202854,0.00807360952260146,0.0560614785016914,-0.0537296337566022,-0.01855819217265,0.0282871578010044,-0.0343078427634531,-0.0864276099408317,-0.104964172205223,-0.117117501342164,-0.0308029438837574,0.047667804732392,0.00122414731216115,0.0195002896291693,-0.00878210129780493,0.0108071853104576,-0.0255005251910606,-0.0275021319773149,0.0633510772697145,-0.0505827825423601,0.028676791057852,-0.00970669370525245,-0.0398098461574422,-0.0411524236677019,0.059967846990109,-0.0518659298511264,0.00416729326692879,-0.0195463928204421,-0.0165253584079164,0.047717311506476,0.186420837478759,0.253722983689357,0.986666036106476,0.308492687798735,0.900940502740108,1,0.670660382366425,0.307630790947162,-0.11091770158094,0.12081208670184,0.00688947040813009,-0.14943036755703,-0.00436458234268827,-0.0194937526067962,0.0538730384303701,0.17352657023769,0.104774852310375,-0.0133957582994491,0.00503676022470549,0.00207750872584546,-0.0468876775725233,-0.0682208813137352,0.026766039723528,-0.139588444345891,-0.0280472808222372,0.273901498086171,-0.196864422284047,0.18128656371097,0.0541585006310249,0.17150514834918,0.00747189257637027,0.126688534776928,-0.00378409494163719,0.159410429237356,0.139424888554442,0.0638970348536547,0.00521910883757246,0.0601764421158101,-0.0611004745534136,-0.0576418739929053,0.139275187315037,0.0673537664721005,0.222253253751134,0.0274799639529289,0.0653555883950752,0.180804897800366,-0.0150512754921765,0.0829922872786322,0.100893754570771,0.079803489748851,-0.0260262717365103,-0.0874198652107806,0.1394760679102,0.0848896318733934,0.147078837687154,0.131713771829789,-0.00555844146627167,0.00154870311602997
## pentanoic acid a,0.0376066163563243,0.00834330605919268,-0.0267833479018829,0.0558519243380635,0.0426182996157321,0.0406572476059164,0.0999665828348479,0.0998233176167243,0.039641150898218,0.0821499693071723,0.00401166834255727,-0.024732900578374,0.0971550113053151,-0.0503598354671056,-0.041340433093485,-0.0726982790318792,-0.069746342534468,-0.0502448262061002,0.000274506389855077,0.0333156571913215,0.107649533012622,-0.0278385105545687,0.0515961323991998,-0.0260376808093493,-0.00301877141147881,0.029458161218325,-0.0415757679558237,0.047266725167765,-0.0369571935006658,-0.0218438033808979,0.0177336178704165,0.0199616989503199,0.0456896725563386,-0.00432046732942366,-0.0253199734275282,0.00735359415156043,0.372487212400147,0.542608551625729,0.481633118552646,0.668207515867263,0.654379238148439,0.598504558535772,0.670660382366425,1,0.659979334581801,-0.0454471068721786,0.094619906737181,-0.0410725638842353,-0.0617157596972537,0.0116764363759363,0.0957863468935797,-0.0263947274697902,0.10902123991358,-0.00344898690809366,-0.0302917674649432,0.0156608510697061,0.00583677613933889,-0.0170424856812938,-0.0950125523666059,-0.073356126572363,0.0740489968533064,-0.0246814199033551,0.0648314307422646,-0.109499038404076,0.146668898182027,0.0228726133109482,0.0877824478284809,-0.0338974519105063,-0.0047455798805997,0.00126342984682187,0.029089715470102,0.126486997284692,0.0522949980307617,0.0243049123903726,0.00682198372897593,-0.0509515678018783,-0.0580293855727298,-0.0936818223315656,0.00650590575696259,0.18704449675263,0.00148868367138379,-0.0359635173044171,0.0095465637098237,-0.0124278785857014,0.0259239311759441,0.00725892812623224,0.0331575076506714,-0.0114493097900065,-0.0833391358282273,-0.00530082628988916,0.0318659648329589,0.0869531705496614,0.062948471774908,-0.05835513044546,-0.00868163744428188
## 4-Methylvaleric acid a,0.0529882061204608,-0.0288857168809748,0.0213014698584518,-0.0124248648961408,-0.0369949028764589,0.0153229602696807,-0.00227095819273064,-0.00907694858924787,-0.0268786402062031,-0.0489221731470889,-0.023531776360098,-0.0221351085456149,-0.017076045860082,-0.00762799328647908,-0.0433975836250966,-0.034214533198523,-0.0348707233690845,-0.00897041173801115,-0.0619420922983623,-0.0639077664208216,0.0208783680829128,-0.035648543145522,-0.00897502055969748,-0.0156788720548184,-0.0790105563624382,0.0460426652469698,-0.0449699750276632,0.0155471112214597,-0.0532329032986255,-0.0378895575425862,-0.073545095516008,0.0462320228421641,0.00881016740940184,-0.0320081885168539,-0.031850724910783,-0.0325119688082755,0.258844130769221,0.339488013906567,0.103294955703103,0.311223609391434,0.997007794969872,0.247640983637422,0.307630790947162,0.659979334581801,1,-0.00840510203855457,-0.0164774887449206,0.0263056792473741,-0.135051051283251,0.0386088204961261,0.18503824153486,-0.01705381210842,0.0333998922569085,-0.0942168907988578,-0.0202084226768168,0.0319333533460069,0.0596768401492818,-0.0458893532705334,-0.0260909591896862,-0.0453304507154524,0.055320638987951,0.0120559631109914,0.0613312132378985,-0.0486742080405823,0.105290679809612,0.076747835888717,0.0563803096657564,-0.0713200535539439,0.00506349636575199,0.00598948884691606,0.0425069112782551,0.221106710751015,0.0359468875510965,-0.0387721174018286,-0.0401051071118924,-0.0875673892413221,-0.0436285782133891,-0.00246812128441865,-0.0173889721546783,0.0777462179897737,-0.0237616774376321,-0.0450646400096265,0.160870178907456,0.061018736145766,-0.0467715983887577,0.216882016265342,0.0547318642890769,0.0114909342007632,-0.0962875443771388,-0.032241277702521,0.121005979410116,0.214455465128811,0.193888303471235,-0.0240740623585174,-0.0284898738362031
## Lactic acid a,-0.125863869590178,-0.186332160473881,-0.0131002924315167,-0.0857434972517397,-0.109323889975839,-0.0235500814728665,-0.109277316566205,-0.0749141369559419,-0.0525117491961227,0.107207586065744,0.0872300071541129,0.0126653328138571,-0.0976377555216196,0.0124743320065695,0.147140723825797,0.0338452463956651,0.0669849002381249,-0.0747901990487953,-0.0735461940764761,-0.0780662338182315,-0.0786852891222483,-0.0627975902574377,-0.144729332069688,-0.0461787627123197,-0.117886206051906,0.0388254223856279,-0.0274886548031592,-0.0560488374875783,0.138576828896324,-0.0173153515801966,0.00865262299428501,-0.0278410977246199,-0.00622595709254898,-0.0885690844862161,-0.0815760730584102,0.0289320285804609,0.303760025863441,0.211359711094845,0.14993390625061,-0.101083400803668,-0.00274579012107999,-0.0175283195539343,-0.11091770158094,-0.0454471068721786,-0.00840510203855457,1,-0.0316562030382782,0.0217180292224208,-0.0781438771815896,0.0545384986479148,-0.030339389871989,-0.0288017242088887,-0.126833964286027,-0.143600688263218,0.0117697452922051,0.114727730323399,0.0149003922099182,-0.0560449431482676,-0.0662596415541194,-0.0148102729216453,0.0480281499852441,0.166073475506396,-0.0430907702272201,0.0613807712711732,-0.0797614632896393,-0.0540490166876848,0.00710435593723816,-0.0126707156535553,0.0068544819791589,-0.0279557166276664,-0.0392394754655039,0.0574493416130211,-0.0211914016736451,0.128708645808972,-0.0257616157939105,-0.120189255644145,-0.0368303297148747,-0.056036172483958,0.00266862999221493,-0.0159476804012795,0.021547056720691,-0.0384574378936304,0.0153525395761388,-0.0220932601257998,-0.0172349453198374,0.106985686899183,-0.0333501921444617,-0.0702132312578814,-0.0174445289459421,-0.0761638516483091,-0.0100091098473271,-0.0720074917682231,-0.0682982265382401,0.000756567078443847,-0.0186194785719662
## f__Acidaminococcaceae,-0.0337628825130373,-0.0430273749007414,0.00716381043062184,0.119608751177056,0.0682119965491398,0.107479601967639,0.0495973274845004,0.0840487922138004,0.109774508964473,-0.00716916000131398,0.0170514023344768,-0.0308648293143876,-0.000294901587100465,-0.0122708997732285,0.0461888350259286,0.0571345786737108,0.0490139104404654,0.04385477387756,0.0786860917281599,0.0760798517323673,0.00611345658185214,0.0245548288841013,-0.0474805428757492,0.0330062946075167,0.0395517813085013,0.0498934970286851,0.0329313497424852,0.0400029895734018,0.0181385418048168,-0.0867800615643949,0.0730127800044649,0.0992002223395458,-0.00992910966101406,0.0283770027998442,0.0592488272898921,0.037078526623695,-0.00432717006183959,0.0115443199876583,0.124380424216554,0.116471420742594,-0.0171135081659378,0.162831490052914,0.12081208670184,0.094619906737181,-0.0164774887449206,-0.0316562030382782,1,-0.0741993016440389,-0.0685283530960082,-0.113629695096096,-0.174863951266735,-0.00454440894554637,0.160518082377904,0.118133233020713,0.031366390649801,0.0104270218069055,-0.0420243742985491,0.0238657056333715,-0.0113597631193082,0.0878347751798368,-0.138566464745273,-0.0249531071459051,0.00788552758149508,-0.147639432129801,-0.00810192812367911,-0.110725074666798,0.0650268506137166,0.199595580212622,0.0262884424880307,0.06931065419685,0.0550364273447448,-0.101364709723488,0.0541327757031467,-0.0329759743965482,-0.0291115460908569,0.152049844989677,-0.0184494541539269,-0.0271378902982038,0.0757243319177321,0.118025235272579,-0.044120858592247,-0.0374464977078178,-0.0170622173087187,0.00283959146843713,0.0405973136945849,-0.0580577984605884,0.101626624776915,-0.0578806835054849,-0.565471806359008,-0.00782794721862588,-0.00837705968460567,0.0193759265814892,0.0115920713239956,-0.0358361973791893,0.107276121083695
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## f__Bacteroidaceae,-0.0522550408000946,0.0541145070457822,-0.0481506216049491,-0.016259705291953,0.000557339384527073,-0.0233467810601134,0.0184684954717301,0.0270683165582608,-0.0222520286382176,0.0485434131373882,0.0906918314683662,-0.016335493465405,0.0409177081090713,-0.0659517025753285,0.0461576350869307,0.00058024929330386,-0.0119662564027594,0.0318301066829539,-0.0201577421278194,-0.0218870702517177,-0.0551532877038911,-0.00676862681412637,0.0379035571645929,0.0166193005933014,0.0506202745918653,-0.0190569108392254,0.0336043472142131,0.0468532128169261,-0.000791932154089913,-0.0175233412119596,0.0146817214993287,-0.0410020570334912,-0.0997270406141221,-0.0219049488839337,-0.023555498558526,0.119859664551344,0.0217272070478794,0.0201429974599525,0.182970904353181,-0.147747840843862,-0.137573550696034,-0.118503685898067,-0.14943036755703,-0.0617157596972537,-0.135051051283251,-0.0781438771815896,-0.0685283530960082,-0.0788227527633563,1,-0.0203178679390099,-0.180326078977369,-0.119090775648803,-0.213825994039434,-0.0337698639758685,-0.076042189638729,-0.0167585108942873,0.0136049047317608,-0.0514046536748353,-0.0910767516003385,0.102589177784169,0.254157071789077,-0.0375879801923542,-0.321262807505404,-0.0313314748026413,-0.172444009548346,-0.200556642703591,0.00263065845093377,-0.552787933913453,-0.288769906625988,0.0428666389718714,0.0215691569916144,-0.323205838200046,-0.0990543052665603,-0.00508823046617947,-0.16593892823832,0.29078365488533,0.0225892771042741,-0.489681852875847,-0.342973256314925,-0.192420285606265,-0.0630416921827832,-0.0749725738504975,-0.518025279602135,-0.159722893766481,-0.0892702770885341,-0.470049052882608,-0.108275623272425,0.0191664668484556,-0.0590921241499667,-0.08679382808408,-0.193022314991773,-0.431534417559866,-0.382003586142248,0.00717892061199216,-0.0416739014474962
## f__Bifidobacteriaceae,-0.193174577276283,0.0174769576625724,0.00563437888385382,-0.0566862243979485,-0.0682653706144379,-0.0190787122204673,-0.122656005236056,-0.071442076514652,-0.00595055101567017,0.0471423362156049,0.0715117411491055,0.0305597051816608,0.00996394952507883,0.0807767102589505,0.120379728573839,-0.0178175251346989,-0.0276358130999827,0.0128498950420707,-0.0233758933370083,-0.0714493305360845,-0.0414048440674157,-0.0334433613017072,-0.0154912906397354,-0.143025706813067,-0.0499888996156664,-0.0660648187084566,-0.101334807831991,-0.041898913969146,0.163912123931285,-0.130931509233315,-0.0300266398606546,0.0628312410604012,-0.114379317853359,-0.0813590464000212,-0.0177809137545296,0.042201849736092,0.0610515898772581,0.0274009015195898,-0.0308967188311683,0.00543213988386957,0.0393353488684622,0.0208888869626697,-0.00436458234268827,0.0116764363759363,0.0386088204961261,0.0545384986479148,-0.113629695096096,0.0819686015333432,-0.0203178679390099,1,0.00679738437273635,-0.0366694117438805,0.256456245461394,-0.0576705627265918,-0.0384840820796333,-0.108146288092171,-0.0555032515571936,0.0130164656330275,-0.0924892200952301,-0.0657229782451028,0.0259626874590494,0.0943257520914909,0.046012639971442,0.0683979480764133,0.0156232788851351,0.194441540622205,-0.113830938723473,-0.143468321591203,0.0150538121239762,-0.0803153002682432,-0.030979233367385,0.161899280787915,-0.0359671455734305,-0.0266589034263535,-0.0646785780628219,0.0541736045460911,-0.0108484876020829,-0.052516320166961,-0.0748946330387807,-0.0715586137190481,0.0463270660757281,-0.0235702530034012,-0.048919725054568,-0.128608623160942,-0.0800385991939702,-0.0586484604786753,-0.0477048597078292,-0.032883679035441,0.0519950700169551,0.00260831926273046,0.0985900179523042,-0.0706926501982156,0.00354427295397068,0.0168733068790159,0.0139265925293678
## f__Clostridiaceae 1,0.138148427168631,-0.0243069549714157,0.016546185103386,0.0762756026979748,0.0382222161983315,0.0732363025429348,0.125298687473909,0.0992984293683952,0.0401137865131812,-0.00155248206679331,-0.073898161068756,0.0344810095533589,-0.0347186041323222,-0.0291820642977304,0.0536827021000011,0.0593110107648778,0.0629868636007617,0.0187928787018505,0.017640638486234,0.0593810044566502,0.0205760541491477,0.0770499923828076,0.188120332052566,0.0394038859957899,0.0708444177232601,-0.0268094855940903,0.0187117666979188,0.0670921798645953,-0.09158816551767,0.154329645625585,0.0205868676238758,-0.0168520550937321,0.109616194210513,0.114149009768994,0.0995800987603306,0.0306224838323836,0.182090474458787,0.199137967634094,0.0833517526682858,-0.0327269690761865,0.180009260193911,-0.0119161811028567,-0.0194937526067962,0.0957863468935797,0.18503824153486,-0.030339389871989,-0.174863951266735,-0.0572415481716615,-0.180326078977369,0.00679738437273635,1,-0.0123232440300932,0.123565270682778,-0.196406186078586,-0.0299424519287306,0.0247873624060811,-0.0408384957216056,0.154046021471565,0.0637031326070594,-0.0442838404523252,0.0904137782757004,0.0765932519840714,-0.0564297285831792,0.292149607907702,-0.0127795028610988,0.527195650518527,-0.141035697308906,0.0685927307737361,-0.0274920581924495,-0.046677376857467,-0.144565526235788,0.0836386664848989,-0.0218049160809462,0.00701245712132721,-0.0176253146626535,-0.101260314712572,-0.0795023592855936,-0.0168841009084613,-0.0490484044262596,-0.022780373862864,0.0124706388456038,-0.0155041517044059,-0.0113773813776237,-0.120898685701515,0.00737030250033228,0.00581057903733236,0.00575909286721245,-0.0676220749217634,0.086670979954778,-0.0867145178043564,-0.0748838869175124,0.088609916801444,0.0455279162175228,-0.117929572777324,0.0346320730496801
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## f__Sutterellaceae,-0.0635593153937235,0.095630122875979,0.12700073790142,0.138914285486151,0.0490783394135659,0.151526882432516,0.0866736989747385,0.0681408115837627,0.0360219989827204,-0.0102332948649083,0.0536379945745382,0.00869068696803594,0.0661884400003094,-0.039291307257633,0.0747443707200723,0.153470553847264,0.118995783264894,0.180555711713452,0.0653552879236595,0.103663157906473,0.08903434379838,0.0445925011958266,0.0340898394233155,-0.0343574804039513,0.142849228905952,-0.0851831556847826,-0.0287529346108697,0.0837137450567922,0.0326331358665673,0.0205751447437593,0.156748347656788,0.0668529056597439,-0.0517589041213755,-0.0476107067910089,0.00830904562520199,0.10452824046852,0.000114201284068335,-0.00111229714751792,0.102526462114511,-0.0753437374892097,-0.0841263205359281,-0.0461589878414422,-0.0611004745534136,-0.0509515678018783,-0.0875673892413221,-0.120189255644145,0.152049844989677,-0.136405426003024,0.29078365488533,0.0541736045460911,-0.101260314712572,-0.0125574395955464,-0.013460041088061,0.16851629652886,-0.041719129930238,-0.102338665808901,-0.0754225278547073,0.0865156990564669,0.00802801225077603,0.121180261122755,0.0794836372794143,0.00555667540843353,-0.125671452186655,-0.0395666640383391,-0.085141806657039,-0.0971172613635883,0.0784425776760035,-0.0712322959255452,-0.13864127671444,0.10408343233576,0.12709283189739,-0.337938835041788,-0.0640932757270644,0.00340905262800681,-0.0525598790708829,1,0.0803543628093013,-0.169568647147137,-0.125524310013584,-0.117472801264796,-0.486699360695914,-0.0502935868266858,-0.344130823628815,0.0693257883839483,-0.0476559494213728,-0.258954217507464,-0.02357658696955,0.112187060007711,-0.0157626214959915,-0.0584661147180107,-0.088257678007616,-0.185295848901867,-0.142595257469395,-0.0942296345517029,0.16005945408355
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## f__unknown_ Bacteria,0.070695933647106,-0.0855278974388435,-0.111247675395206,-0.143835709522316,-0.0464134271875209,-0.16080188541736,-0.133740740670018,-0.149548523999952,-0.0647585099883699,-0.0428922828216581,-0.0272992149206293,0.00519546520807276,-0.0715862466507157,0.00131217811585294,-0.157927746462342,-0.127755485358632,-0.119155218691794,-0.0841612248629031,0.0305469623044426,-0.0546626963467371,-0.0389488265036985,0.0101459785787494,-0.013796640479297,-0.0184630752829613,-0.0854439075123554,0.12702197441401,-0.0650770039402848,-0.104167588717396,-0.0260603847908034,-0.0691045458923854,-0.186333218709354,-0.0165800847286485,-0.062706365283512,0.0170546491955391,-0.0341836950836401,-0.0845740173862706,-0.177371829213373,-0.224185195921025,-0.35263858336186,0.130326021158363,0.000738446793285618,0.103122795861221,0.139275187315037,-0.0936818223315656,-0.00246812128441865,-0.056036172483958,-0.0271378902982038,0.0752487041906988,-0.489681852875847,-0.052516320166961,-0.0168841009084613,0.0148091691087044,0.00648715328635663,0.125446757474153,0.052745316199696,-0.0230964958222307,-0.0205381224272692,-0.160574907856782,0.139269941737036,-0.0672507947745891,-0.423084958792087,-0.0505149817564136,0.450412758139412,-0.0891155556909263,0.0622032864132999,0.0721488869981261,0.236577633512315,0.076108906660173,0.255299163256486,0.158404899782706,0.245993559366833,0.324827089402365,0.0764436107293226,-0.150554799760047,0.00963316587034351,-0.169568647147137,0.186313572165097,1,0.186836518837586,0.119637176505575,0.0315225427765252,0.193386528479126,0.634691584199538,0.172920754950035,0.0895724840151358,0.582694668347113,0.216676905399797,0.174605387111133,0.0425347894464647,0.270500251577194,0.241548912417982,0.445254706617996,0.423397734125143,0.117523989772316,-0.122342347024249
## f__unknown_ Bacteroidales,-0.0212742791134975,-9.85030097477337e-05,-0.0667046900954158,-0.128313148548098,-0.0881738082096117,-0.102034403414214,-0.0943038979479018,-0.111610813448538,-0.0879007674556568,0.0119372487405395,-0.131011976441311,-0.029118940625083,-0.0708308657855504,-0.000835923458772629,-0.0679579322370015,-0.03509625125302,-0.00960879496185386,-0.0887152056177452,-0.0134531671363929,-0.0197882905893614,-0.0132176315122289,0.0451611765778173,-0.039448759980022,0.0835248072306721,-0.0889610433092474,0.0254718441412762,0.0931817348009988,-0.0228048794244805,-0.00951702307194652,0.0129108410206683,-0.107060519003791,-0.00452022863319777,-0.111224330523616,-0.0453542902576893,-0.0513879236458354,-0.0319555720404804,-0.0423231006562109,0.0565558568378281,-0.0790394328050164,0.0606581772993886,-0.0180452943898788,0.0318050011297583,0.0673537664721005,0.00650590575696259,-0.0173889721546783,0.00266862999221493,0.0757243319177321,0.0787698578101907,-0.342973256314925,-0.0748946330387807,-0.0490484044262596,0.268560696876701,0.0369961584351264,0.24552397488987,0.303322062372546,0.0633579989305716,-0.0118222440481211,0.0307209842254723,0.0769114041943535,-0.0227471614188859,-0.177168208898241,0.0209980899450516,0.194407259557094,-0.0332322448503712,0.0771201862976805,0.0129727329790819,0.0809064748570375,0.216111846420646,0.234285552083633,-0.0170027413067351,-0.117210078415531,0.0786003401189669,0.16831439494658,0.0219821276036412,0.00402818539736525,-0.125524310013584,0.00545025089220379,0.186836518837586,1,0.198506665055925,0.0719387399941544,0.140234374562921,0.259418291229678,0.14450236478077,0.117931294845903,0.221173491880636,0.125821138796478,-0.0577926651306047,0.0243799538723269,0.126514488399453,0.144281247331148,0.240023974792999,0.20533589979,0.0851825333791767,-0.0998173341733198
## f__unknown_ Bacteroidetes,0.0201536422231337,-0.0414043648689914,0.0716788947789419,0.106058039455546,0.0414475447407864,0.112183594075227,0.0580197375936793,0.0625949260885474,0.0544464435252283,-0.0900816382080169,-0.0170095353934039,-0.00917024663271122,-0.0544565881409054,0.0198333387562507,0.0230113201017024,-0.0204953012923725,-0.0208760101089507,-0.00787971079490874,0.0787693110938571,0.0532248859303253,0.0336591985969847,0.0733725076541558,-0.037263347076892,0.0293471205179208,-0.0151366072100621,-0.0395691710606982,0.0577448592738027,0.0319288925031854,-0.0225744440791718,-0.0390981718152012,-0.0256799903925681,0.000767366645644657,0.0130095984416819,0.0179629914599309,0.0551355316256867,-0.0814618059141526,0.0747378667294589,0.0913859141482798,0.0602435984924073,0.21095891011596,0.0750438494806153,0.18197244522596,0.222253253751134,0.18704449675263,0.0777462179897737,-0.0159476804012795,0.118025235272579,-0.0161779023948668,-0.192420285606265,-0.0715586137190481,-0.022780373862864,-0.0106674854539376,0.164274735647655,0.00316966950476293,0.0109420381938107,-0.0202361741748615,0.0016661872226276,-0.00691628673048042,0.0370295771785807,-0.0142654974387107,-0.0896590830437254,0.0672771150288206,0.140980334237982,-0.0547891610673891,0.0226329414284355,0.0568652574715464,0.0213613153533016,0.106366655808417,0.0893660319007104,0.00616134968597834,-0.054350537253086,0.0589696716237412,0.0696902778695629,-0.0614959453333765,0.00464579976348024,-0.117472801264796,0.00375215281672031,0.119637176505575,0.198506665055925,1,0.0428964933487311,0.000824210704673879,0.17471164875653,0.010800473076753,0.0453872603897403,0.157681103717773,-0.00896762462722645,-0.024026102813083,-0.0526866973186445,0.073283337508265,-0.00672846971744995,0.0885827322855591,0.0298416148437054,-0.0487947252794622,0.129441561501406
## f__unknown_ Burkholderiales,-0.0126506164351598,-0.0250280583420901,-0.0423362429151389,0.00666337550557607,0.06586607890722,-0.0489878551538031,-0.00183502916694229,0.0537780109642693,0.0737609126844342,0.0247283838465716,-0.0360760037383968,0.00334539710050104,0.0393827599452673,0.0214321851064496,0.0524701865560724,-0.0704956067929096,-0.0533089327371406,-0.0934351604800104,-0.0162506413372299,-0.0125164949463898,-0.0159168120561121,-0.121690911379916,0.0605758515146507,0.0422664089254019,0.0197952022679208,-0.0610417307462024,0.0675331430841561,-0.00134088740990384,-0.00324378015337884,-0.0223124140182722,-0.00743290881156664,0.00326355623799906,0.0722349588904449,-0.0350954059931169,-0.042402804481282,-0.0489495802797117,-0.0204483906221738,-0.0117679576100281,0.0130605111959126,0.0361362268174009,-0.0263954774217103,0.0266392456145783,0.0274799639529289,0.00148868367138379,-0.0237616774376321,0.021547056720691,-0.044120858592247,-0.00823664700877869,-0.0630416921827832,0.0463270660757281,0.0124706388456038,0.0340248404155834,-0.00949738879994542,-0.0447765505424449,-0.0235308833683261,-0.0931001504169542,-0.0316137734688666,-0.0212487228566543,-0.0121654751501498,-0.0400196103099239,-0.00463685353142214,0.029166270925269,0.0228885113995672,-0.0252752135714964,0.040432265455702,-0.0220977379812723,-0.0226486273424119,0.0601996247340153,-0.0131336882019316,-0.0348695646411636,-0.0662204604533838,0.0839132681871976,0.0273720017402007,-0.0408256613164692,0.0216742724315652,-0.486699360695914,-0.0247553452422167,0.0315225427765252,0.0719387399941544,0.0428964933487311,1,-0.0246721348201117,0.0885096120273814,-0.0506251633276254,-0.0433814328180483,0.00698585019452063,0.0286351013959469,-0.010541449150683,0.128024177676896,-0.0182560648056888,0.0245178433263651,0.0744373057817556,0.0698202955246034,0.0496362142761599,-0.071752424806706
## f__unknown_ Clostridia,0.0141386101393679,0.00656090936293092,-0.0824629801110609,-0.0726343769902047,0.0125860945675021,-0.113122513001675,-0.0319865724723312,-0.0312575183389046,0.0236401032086536,-0.0121329576029897,-0.0236691842364022,-0.00897339201737536,-0.0165127330242701,-0.0420747131779136,-0.0341909081353208,-0.133014390339852,-0.144013712610458,-0.0298327638506231,-0.0567641179712897,-0.0501162013606338,-0.032978695560581,-0.00959004926551564,-0.0316175370657816,0.0379268830311074,-0.0586263428713612,0.128234103824436,-0.00853792677245702,-0.101085129347092,0.0288455020210714,-0.00661942986614939,-0.0826121745308028,-0.0530393382755023,-0.0459295007716909,0.0414403978718254,-0.033353370620603,0.0639454627617467,-0.0250177726411095,-0.0496173657505923,-0.0868454753216309,0.0639771355551443,-0.0450271911055889,0.0529958942215383,0.0653555883950752,-0.0359635173044171,-0.0450646400096265,-0.0384574378936304,-0.0374464977078178,0.0608406032535242,-0.0749725738504975,-0.0235702530034012,-0.0155041517044059,0.0296586769318764,0.0105102837642421,0.120031539971829,0.279222564840284,-0.00460405045861746,0.0327850639381377,-0.0539054022033985,-0.0191088657074934,-0.0109957686506645,-0.147065704312517,0.035350348306201,0.10776164456882,-0.0144538180449278,-0.037635499262865,0.0254781018782437,0.0565332519762242,-0.00383358584399232,0.0744988407630496,-0.0100665767151252,0.0866151291890382,0.0589712381701601,0.123263726041209,0.0748951840646754,-0.00995045187172392,-0.0502935868266858,0.00973827512453991,0.193386528479126,0.140234374562921,0.000824210704673879,-0.0246721348201117,1,0.142786012941553,-0.0214057747495563,0.0710244945626812,0.117007794511628,0.0082594040705428,-0.017824529809861,-0.00671566866647692,0.0149053847041712,0.122226066313563,0.0853508473896767,0.0504176430421002,0.0889275837554378,-0.0722299309317572
## f__unknown_ Clostridiales,0.156764949799439,-0.101299296985294,-0.0967293547385683,-0.167711442175838,-0.0735385339173505,-0.170276892697067,-0.146096366236215,-0.143526770732447,-0.0681253697119656,-0.0336800618632054,-0.130518505149291,-0.030024912791502,-0.129030344487903,0.0385964250550266,-0.205853603861922,-0.142990563078257,-0.12672820528242,-0.11733167921786,-0.0560828098340107,-0.177676903743082,-0.0998036712667443,0.0118875030626587,-0.12486771164734,0.0505199734018422,-0.143662151493243,0.170923939989618,-0.00975728834247895,-0.117328249316393,-0.094588648071942,-0.046597124126416,-0.192099140959646,-0.055910809303695,-0.120957424832532,0.0673041149177563,0.0176165745234091,-0.0987462171562396,-0.109387915380571,-0.195980573974911,-0.388429481011648,0.173364151252765,0.165219779847449,0.134984749602082,0.180804897800366,0.0095465637098237,0.160870178907456,0.0153525395761388,-0.0170622173087187,0.12536836067745,-0.518025279602135,-0.048919725054568,-0.0113773813776237,0.0822728910111253,0.0457430663502789,0.087919984510204,0.108010248080037,0.0405813043311313,-0.0273061393264091,-0.15952167537476,0.105996675195913,-0.108513562379663,-0.335067114233781,-0.0335546775171603,0.421985044097864,-0.142387777648521,0.138253634497046,0.0637062066812888,0.280354926942709,0.0588391754316142,0.323613146676951,0.0126160935287761,0.253400262060506,0.487132756823117,0.0899318907621084,-0.0909830808782827,0.0162168650733372,-0.344130823628815,0.0745995372229844,0.634691584199538,0.259418291229678,0.17471164875653,0.0885096120273814,0.142786012941553,1,0.204671877398574,0.103662250540379,0.689940668719646,0.139157047239362,-0.0101583670772657,-0.112994951835664,0.303151447592521,0.295114225069409,0.60682549798717,0.549123891024294,0.134367015006114,-0.156454680592097
## f__unknown_ Deltaproteobacteria,-0.0142489503545086,0.0454125347061092,-0.042624357738487,-0.0949655159710579,-0.0513140742417067,-0.0878512678633732,-0.116896529994423,-0.123345723160709,-0.0740287767397988,0.0130647031061242,-0.0267100862156475,-0.0079942161867724,-0.0417480127626138,-0.0530519037889053,-0.0137696883760239,-0.0104393653855411,0.00503796825216528,-0.0409041652736601,-0.00081486570084009,0.0124106251048386,-0.0755548562408369,-0.027160197788405,-0.0702986715594967,-0.0203569004979897,-0.0517675656419915,0.0265244534290438,-0.0153637491499817,-0.0554221358331169,0.0166995542203283,-0.0628162513539249,-0.0883500187570228,0.0160743419698159,-0.0914575231401548,-0.0911482468160587,-0.0506705548465069,-0.0259416204352749,0.0107370587464708,-0.0189759903009309,-0.128009570834082,-0.0163543613465746,0.0649735198444059,-0.0263138108490669,-0.0150512754921765,-0.0124278785857014,0.061018736145766,-0.0220932601257998,0.00283959146843713,0.0152711808662186,-0.159722893766481,-0.128608623160942,-0.120898685701515,0.0290416008822092,-0.100112431702891,0.152680359965564,-0.0207363664641675,-0.0398831543202198,-0.0369548555110702,-0.041372156219428,0.141060533376748,-0.0491203054255011,-0.0130838223692714,-0.100922102876807,0.0625490422318976,0.0264074034643083,0.00465588834673633,-0.0990000954046267,0.167688312191526,0.0215921202883772,0.0534354067497627,0.101579067912691,0.0911433100052371,0.154740473812098,0.0562484982218576,-0.0830388064529329,-0.0357205388346755,0.0693257883839483,0.116406471434435,0.172920754950035,0.14450236478077,0.010800473076753,-0.0506251633276254,-0.0214057747495563,0.204671877398574,1,0.0271056793536807,0.230130067846423,0.0452121258128849,0.0520184738411781,-0.0211149541626085,0.053347947098127,0.0172151915587713,0.281769535539577,0.293432771762202,0.0852424239981184,-0.104059034498752
## f__unknown_ Desulfovibrionales,0.0617759031714565,-0.0433539522828248,-0.0117524746225325,0.0371704550006995,0.0838088470744732,-0.0220600835205295,0.0595629099486169,0.0619109750343958,0.0110678907335948,-0.00863826529135102,-0.00336258810591843,0.0134465847259518,0.0780041270714912,-0.0479900939731942,-0.0440913735697803,-0.0950241017834416,-0.0955291503375299,-0.0408126073541629,-0.0321407669400017,-0.0361564033975163,-0.0452849442790668,0.0171394486201833,-0.0133198257564181,0.0406209127610543,-0.0292086586035565,-0.024308103514758,0.0660822593792879,0.0399346706460126,-0.108878432231042,0.0448721868646204,0.0159576777743425,-0.0737534280375419,-0.0192334132725823,0.0219826802441747,0.0360277503611793,-0.0894407887513698,-0.0554162144938745,-0.0469156622334224,-0.0585757630006605,0.0705083789505147,-0.0470209902422969,0.0410294296739098,0.0829922872786322,0.0259239311759441,-0.0467715983887577,-0.0172349453198374,0.0405973136945849,0.0946883764408545,-0.0892702770885341,-0.0800385991939702,0.00737030250033228,-0.0164802971541847,0.0482780666054014,0.0918434647458046,0.0234382287466332,0.0143143735835349,0.02970712495517,0.0315916935378037,-0.0381143225399642,-0.017481060038443,-0.0154051753396013,0.0507408583223495,0.119938435065261,-0.0455557617552447,0.0472588871627914,0.0281559714831658,0.0168202156307875,-0.0361925518459489,0.350286014390927,-0.0265729714420229,-0.00876572623981444,0.0536611360415263,0.0634344180846778,0.0385074761244177,0.0240698120594307,-0.0476559494213728,-0.0616180043746284,0.0895724840151358,0.117931294845903,0.0453872603897403,-0.0433814328180483,0.0710244945626812,0.103662250540379,0.0271056793536807,1,0.0663719535206339,0.00441311571328154,0.17710839020694,-0.0455539845641783,0.126299607382913,0.116498898096295,0.136740652262789,0.13327087802016,0.0520755369360882,-0.0324322320370311
## f__unknown_ Firmicutes,0.0579856702810597,-0.113979454141089,-0.0529789508436558,-0.152861420296728,-0.0754422060527611,-0.147761238089637,-0.160425997430756,-0.155653528528066,-0.0888904862459868,-0.0790694825918823,-0.134684250797498,-0.0213150844932326,-0.136539573084584,-0.0067973464639144,-0.125304071193874,-0.141820795374608,-0.126284806163011,-0.109429163160048,-0.0937115969355736,-0.14951441720999,-0.0927156337464429,-0.0398377822660419,-0.103749620237521,-0.0325239938686947,-0.186707600977266,0.0928533921630947,-0.0607079772761177,-0.15257247026992,0.00527550544718023,-0.0499711679743285,-0.221173500302759,-0.0454602079527184,-0.1081066329239,-0.0195420365861132,-0.0405703867809975,-0.104620686343199,-0.0544801777993989,-0.126530954297898,-0.347321714371023,0.0932717844771715,0.220527584798625,0.0708667704890086,0.100893754570771,0.00725892812623224,0.216882016265342,0.106985686899183,-0.0580577984605884,0.0688507915203363,-0.470049052882608,-0.0586484604786753,0.00581057903733236,0.0974899758094414,-0.00596342759911282,-0.0144666721700933,0.0829030850167253,0.0812820250113578,0.0632703962370646,-0.138573680503546,0.141723829715783,-0.0934283560671834,-0.272202474399606,0.0103073444117399,0.360872193957446,-0.0106916709273031,0.0755858154461293,0.101656129410509,0.266541417086918,-0.0338629233965564,0.314709011335936,0.0284116405980425,0.27693885886654,0.463497172466636,0.0894435391877884,-0.0605734043860504,-0.0298257553486118,-0.258954217507464,0.139060262942377,0.582694668347113,0.221173491880636,0.157681103717773,0.00698585019452063,0.117007794511628,0.689940668719646,0.230130067846423,0.0663719535206339,1,0.0417872940975383,0.0912930439531177,-0.131691561212454,0.236345570856651,0.199903886462472,0.567623621631508,0.519541485860801,0.130328883641286,-0.136256469238089
## f__unknown_ Proteobacteria,-0.036629614976783,0.00095806542812103,0.00443126291821354,-0.0943408155877271,-0.146179196982006,-0.00293877769029672,-0.0958336452637264,-0.101045270453363,-0.152747701319113,-0.0595364941628083,-0.0821799826199814,-0.0106696902195912,-0.0730957722229454,-0.0455123015345965,-0.02085564142015,0.00508575744285391,-0.00664111562989089,0.0422758660996351,0.0652059931007402,-0.0211996845904619,-0.0553256995826815,-0.00942236778042618,-0.0216164922938576,-0.0403733275766421,-0.0735956562461873,0.0891150557952695,-0.0859389654135322,0.0171329611983413,0.0387341531591934,-0.038509355194571,-0.0333973668930977,0.0667246946358373,-0.0359937097810155,-0.0946903773058388,-0.104413321490275,0.00145566730604256,-0.010691789303417,0.00212766047839817,-0.027632136193234,0.0889227236560874,0.0556185487905652,0.0744831005309429,0.079803489748851,0.0331575076506714,0.0547318642890769,-0.0333501921444617,0.101626624776915,0.0236469785255768,-0.108275623272425,-0.0477048597078292,0.00575909286721245,-0.0124433374132981,-0.0627650293571015,0.0385873369584076,0.0755961512631415,-0.0376121486321294,-0.0195167212522614,-0.0161435386734242,0.0323432586323992,-0.0131501482286156,-0.0847186300440784,-0.0258161490322326,0.0184478836921733,0.00210043255730621,0.0517392889696117,0.0209709586047732,0.162080416346166,0.0307354278616357,0.17994316785311,0.092408793599937,-0.0244503552745336,0.0410335130737007,-0.00866396369690481,-0.0851858893136434,-0.0104588800621214,-0.02357658696955,0.131337349470728,0.216676905399797,0.125821138796478,-0.00896762462722645,0.0286351013959469,0.0082594040705428,0.139157047239362,0.0452121258128849,0.00441311571328154,0.0417872940975383,1,0.035665265358814,-0.0318780471403248,0.0378990368960202,0.0654154404608551,0.114088557452764,0.128840053939237,-0.0357371555239407,-0.0567939314242077
## f__unknown_ Rhodospirillales,0.107333647484019,-0.000952125098733892,0.00107872237990128,0.0381255094610412,0.0865147373810685,-0.0231124006704273,0.0317860318240314,0.0278367915429846,0.00572349770839562,-0.102366824670969,0.000314900905676963,0.0160896545027167,0.11917633471665,-0.00796352725459156,-0.101296448459335,-0.00691997244709664,-0.0332519770025051,0.0777245894750881,0.103459378598414,0.118015510809735,0.08620652035773,0.0812831006781524,0.070825913898388,-0.0334282851413789,0.0954019215939902,-0.056029653632464,-0.0361110176755336,0.0554690109942724,-0.122213838994105,0.0898647953055508,-0.000417778152799829,-0.0406283733554546,0.14726580700891,0.0633536126387731,0.0248412139723888,-0.0663156958141818,-0.0361175265521343,-0.0811452373910057,-0.0881395628091863,-0.0340126203305344,0.012747552626375,-0.0404803511226347,-0.0260262717365103,-0.0114493097900065,0.0114909342007632,-0.0702132312578814,-0.0578806835054849,-0.0474784185045975,0.0191664668484556,-0.032883679035441,-0.0676220749217634,-0.0259470303483929,-0.0318928042860949,0.112880311339704,-0.0232462665263496,-0.0212798561194339,-0.0122091341023032,-0.027255362027469,-0.00501572517652458,-0.0320546079252707,-0.0441051491181694,-0.0588804077777855,0.00248371604290178,-0.0188953824480881,0.0197454741505443,-0.0752865178008612,0.159677802202156,-0.0892401602547242,-0.042142486661712,0.0448909584210946,0.0813899328461063,0.0245084576708627,-0.0213287019783323,-0.0275260221951407,-0.0255611045827914,0.112187060007711,-0.029672520167545,0.174605387111133,-0.0577926651306047,-0.024026102813083,-0.010541449150683,-0.017824529809861,-0.0101583670772657,0.0520184738411781,0.17710839020694,0.0912930439531177,0.035665265358814,1,-0.0212617758024149,0.0964577793442888,0.00205271940268221,0.0314753682754806,0.038228599838671,-0.00610669390530455,-0.035991642046431
## f__Veillonellaceae,-0.0548827053033902,0.0430038358860277,0.0650844642702941,0.0616604681263811,0.0233298962374974,0.0659245675236489,0.0629935454175333,0.0426713641243096,0.0250089098046042,-0.0394830410191565,0.0134215991606647,0.00460656675082397,0.0384158037734345,-0.0111654042353362,0.0690204407118846,0.0521713715335351,0.0397999746493502,0.0674618515529052,0.133521421453585,0.186616810762576,0.145593262837596,0.0469584956727032,0.183651756877206,0.0367286393405909,0.180582130724839,-0.0988295076031066,0.041785015769476,-0.0536736964130929,0.100758203450602,-0.00281776749880743,0.0523930006430508,-0.00167547077737046,0.045006101944683,-0.0401795904858022,-0.0046753608563755,-0.0603579346241633,-0.0217523743320743,0.015647922418825,0.0915907567034642,-0.0821070260038158,-0.0956706646350466,-0.0633001946089275,-0.0874198652107806,-0.0833391358282273,-0.0962875443771388,-0.0174445289459421,-0.565471806359008,0.0325224222176398,-0.0590921241499667,0.0519950700169551,0.086670979954778,0.0510914419490814,-0.0484845409073393,-0.00326359670112944,-0.026357766433107,-0.0272186871364121,0.00268733669597664,-0.0247354497692176,-0.045818542176425,-0.0705360832574507,-0.099366222746256,0.0219937249314334,-0.034732405833827,0.0747650712998592,0.0327251033955574,0.0398391091227011,-0.182153300520057,0.12483082123882,-0.0184469155340613,-0.0219182064145692,-0.190963027994832,-0.183736014285097,-0.0603405026614916,0.0298721209306319,0.0798865775630916,-0.0157626214959915,0.0164628229093449,0.0425347894464647,0.0243799538723269,-0.0526866973186445,0.128024177676896,-0.00671566866647692,-0.112994951835664,-0.0211149541626085,-0.0455539845641783,-0.131691561212454,-0.0318780471403248,-0.0212617758024149,1,-0.0210991126360099,-0.00923999037171129,-0.156059399463277,-0.103258545303252,-0.0714927353232074,0.0656083164793164
## f__Verrucomicrobiaceae,0.068030286075855,2.65047533915927e-05,-0.0581851267002705,-0.0698948531314221,0.0102546224270369,-0.107230252246607,-0.0308293785837023,-0.054496637301595,-0.0351990310067782,-0.00625460105021475,0.0305567612308509,0.0963312885990872,0.0895600172760087,0.0135595579024554,-0.234070734000742,-0.114917580004485,-0.0926209609559386,-0.130581056968397,0.00827205504133224,-0.0146304528002563,-0.0588813071677988,0.0508413913882128,-0.00574623096565277,-0.00797297894980834,-0.0362997485886526,0.0314792101358152,-0.015926134229815,-0.0538577963239445,-0.0449717999232484,0.0295684764588664,-0.0345743462856489,-0.0781438735307493,-0.105664711563957,-0.00876355371977187,-0.0226965148964878,-0.0847834198677987,-0.142339511040283,-0.153184947737229,-0.153636527522735,0.145356206217962,-0.0254012245484089,0.117584969156899,0.1394760679102,-0.00530082628988916,-0.032241277702521,-0.0761638516483091,-0.00782794721862588,0.21786478878212,-0.08679382808408,0.00260831926273046,-0.0867145178043564,0.0303764911613398,0.00507661239619644,0.168475824196967,0.0320771184212489,-0.00937167511231174,-0.0313833865425916,-0.181400178359853,0.0483447230539115,-0.0233315478053375,-0.320891969240412,0.0301792906487716,0.112782276885872,-0.157538127188841,-0.0661031103821734,-0.0181814529494582,0.176852942742644,-0.0769297380576656,0.108260507191926,-0.0241328435557285,0.186066543340197,0.118012747327106,0.0845366631169111,-0.141756364342073,-0.0128229177353962,-0.0584661147180107,0.0915849095894833,0.270500251577194,0.126514488399453,0.073283337508265,-0.0182560648056888,0.0149053847041712,0.303151447592521,0.053347947098127,0.126299607382913,0.236345570856651,0.0378990368960202,0.0964577793442888,-0.0210991126360099,1,0.0834232472884384,0.138491299217778,0.153328440654547,0.0862303199053292,-0.0972852470329518
## f__Victivallaceae,0.0397160897827812,0.0153568572640554,-0.0743855794651706,-0.0704804173314743,-0.0200398481306225,-0.0811871403144304,-0.0628971562242779,-0.0439446238932288,-0.0140774894222489,0.0213687907097353,-0.0073095022557472,-0.0145943032201946,-0.0651483890720279,-0.0117435358012184,-0.115889716851436,-0.0825305534450734,-0.0692853459589068,-0.0718904842891018,-0.0745217450125637,-0.104435150093392,-0.07408958272715,-0.0121797063500422,-0.0530636315341931,0.0211710710279287,-0.0611607589982681,0.0535546717935757,-0.0188072973222807,-0.0459279374295939,-0.0483894342115421,0.0231767947311235,-0.120017772442134,0.00889382322513383,-0.0995807562906505,-0.0412604289209078,-0.00469743894886972,-0.0976678740756682,-0.058559953851604,-0.0789017245698165,-0.131213206819088,0.0830418958881578,0.115459964764221,0.0469425045033971,0.0848896318733934,0.0318659648329589,0.121005979410116,-0.0100091098473271,-0.00837705968460567,0.165927441885155,-0.193022314991773,0.0985900179523042,-0.0748838869175124,0.0097343571123978,0.117220919603621,0.163246810361832,0.0730454444328155,-0.0276774988039766,0.0163677821790969,-0.0765668967833146,0.0261023508029281,-0.0336010711066908,-0.205330942373478,0.0217055665707188,0.150383449412338,-0.070178750980067,-0.0378058978349833,-0.0740535143437704,0.0895748419785223,0.068910635893436,0.180171794629046,-0.00647786863280463,0.0700123987498614,0.176743835370349,0.0244150306827698,0.0592003905339584,-0.00800758215059213,-0.088257678007616,-0.00783301776608451,0.241548912417982,0.144281247331148,-0.00672846971744995,0.0245178433263651,0.122226066313563,0.295114225069409,0.0172151915587713,0.116498898096295,0.199903886462472,0.0654154404608551,0.00205271940268221,-0.00923999037171129,0.0834232472884384,1,0.222320316967649,0.185200191133404,0.0983127235013773,-0.0701347066909341
## Shannon.effective,0.118744178965278,-0.0426670117438889,-0.0849658074386007,-0.128363524932325,-0.0237637954658437,-0.159167943007718,-0.108097106474971,-0.114327220232302,-0.0263117636267456,-0.03427268623384,-0.106400266288141,0.00518048139529498,-0.0561592738232624,-0.0433921287709359,-0.133407060932367,-0.140450283993041,-0.128075377004168,-0.0986346478487858,-0.0887300673208662,-0.156039531259622,-0.072024544960198,0.0139273564353276,-0.0686904647943995,0.0283111709768033,-0.207076529986264,0.162061817611649,-0.017195198498842,-0.0659600044062179,-0.0997449391821805,0.0106122283470918,-0.169328592329173,-0.0279966841027492,-0.104116652434683,0.0694818336890962,0.0243997116770987,-0.115500677906575,-0.0928706082944952,-0.128079002438291,-0.360147428821021,0.133424616746606,0.219332794762261,0.0942636399139544,0.147078837687154,0.0869531705496614,0.214455465128811,-0.0720074917682231,0.0193759265814892,0.00800204297244123,-0.431534417559866,-0.0706926501982156,0.088609916801444,0.0964389219739194,0.149076841026041,0.155230756744251,0.149193198596616,0.0121908752309888,0.000237709291037098,0.0223986492080752,0.180289808597804,-0.0817715278900114,-0.037841300426017,0.0380603962566917,0.247991788197309,-0.0793535732064569,0.153754368613503,0.172594696470625,0.336741367435293,0.0504025771564949,0.273677568387802,0.0513090583336654,0.34164009864334,0.60160046135508,0.0766474300276419,-0.00484412004924405,-0.00781256028991735,-0.185295848901867,0.0521087335850304,0.445254706617996,0.240023974792999,0.0885827322855591,0.0744373057817556,0.0853508473896767,0.60682549798717,0.281769535539577,0.136740652262789,0.567623621631508,0.114088557452764,0.0314753682754806,-0.156059399463277,0.138491299217778,0.222320316967649,1,0.925782508927055,0.162479482851898,-0.147404702369035
## Simpson.effective,0.080644555290159,-0.0432720956505935,-0.0886374362809392,-0.131912564558257,-0.026579650622505,-0.161647073114767,-0.113635984590586,-0.116040773296618,-0.0281089143232601,-0.0261915165161485,-0.0548851182810317,0.00361172397425259,-0.0463715659115747,-0.0278592680877378,-0.113722751755173,-0.12238462314916,-0.105212154777459,-0.105890312547024,-0.0573739464812142,-0.121128600005673,-0.0571234346315914,0.0145798691718731,-0.0666017034129571,0.0202024939149536,-0.151822573583164,0.146612798733963,-0.0344373463685929,-0.0646491039979221,-0.0803293996128726,-0.0228635067715788,-0.151200176346972,-0.010493529416907,-0.0968374368525472,0.0682373189412681,0.0424957408373283,-0.0762838743253361,-0.108889084391714,-0.138986129926731,-0.345626096030621,0.114632486456763,0.198723467920976,0.0780938481855311,0.131713771829789,0.062948471774908,0.193888303471235,-0.0682982265382401,0.0115920713239956,0.00615847766243073,-0.382003586142248,0.00354427295397068,0.0455279162175228,0.0791824506978132,0.134978260982361,0.161310642737569,0.157590138491256,-0.0229548462721463,-0.0164696669546669,0.0559221550551026,0.179170650841721,-0.0448227231607443,0.0435979959388365,0.0305044277850269,0.225844611459465,-0.055086999600826,0.161195244449393,0.156565376355421,0.27750359346858,-0.034170284412016,0.265337007771572,0.0419285833344118,0.274003780397439,0.531769060063879,0.0609184607831012,0.0244443968531274,-0.0122088100857236,-0.142595257469395,0.0873416091715541,0.423397734125143,0.20533589979,0.0298416148437054,0.0698202955246034,0.0504176430421002,0.549123891024294,0.293432771762202,0.13327087802016,0.519541485860801,0.128840053939237,0.038228599838671,-0.103258545303252,0.153328440654547,0.185200191133404,0.925782508927055,1,0.161061235721758,-0.127679345253728
## Sex (f),-0.0595777470409746,0.00346011792904233,-0.697779169208974,-0.509747996654153,0.132182725145674,-0.832744630502507,-0.454822907508006,-0.380763182671027,0.0368229352953622,0.137530872494534,0.137909091633462,0.116654037029173,-0.0247241407054695,-0.0336976691683666,-0.389248797028189,-0.635105693382232,-0.603200180163915,-0.414328185897121,-0.161797336417842,-0.329075309615122,-0.331799950231292,0.0470065269484211,-0.196469941152273,0.166717879970144,-0.189041767983853,0.475009319647746,0.0285415758629075,-0.574934136282446,-0.0169711653652572,-0.281534893704587,-0.575148541072422,-0.193503815039119,-0.419672245014789,-0.295960513167008,-0.165223698481579,0.15778652581411,-0.132587500627366,-0.196469238392555,-0.21733499780524,0.0090013873618995,-0.0179829185251035,-0.00483032194204923,-0.00555844146627167,-0.05835513044546,-0.0240740623585174,0.000756567078443847,-0.0358361973791893,0.0628210225152164,0.00717892061199216,0.0168733068790159,-0.117929572777324,0.0668781834708385,-0.0973661892123586,0.0917658581393759,0.0644200634300011,-0.078095870990036,-0.0625852483400591,-0.0686184215634092,0.0154733526258412,-0.0249453987998564,-0.0295068410632009,-0.0141330582826446,0.0376174391913539,-0.030806543424062,-0.0600537021926844,-0.0248533765103763,0.139917023159038,-0.0645880158325606,0.0661263707260523,-0.08095790142245,0.128153990751882,0.150271025409467,0.0536087319074491,0.0458672729528574,-0.0567394652624697,-0.0942296345517029,0.0631164945088566,0.117523989772316,0.0851825333791767,-0.0487947252794622,0.0496362142761599,0.0889275837554378,0.134367015006114,0.0852424239981184,0.0520755369360882,0.130328883641286,-0.0357371555239407,-0.00610669390530455,-0.0714927353232074,0.0862303199053292,0.0983127235013773,0.162479482851898,0.161061235721758,1,-0.658352497000943
## RMR,-0.184412759666658,-0.147487047870104,0.706292450492882,0.722217338567701,0.181632132486318,0.853038725917889,0.456396095509878,0.492854323111926,0.349196998570865,0.0512902508975052,0.0588271686904903,-0.0580417636820717,0.159350394468411,0.042920104187761,0.404417523995975,0.537744197721457,0.484147722903868,0.422277012543843,0.170503185660364,0.343004608687763,0.251291820204052,-0.00198542159376624,0.184952763299143,-0.199284713230051,0.279381235248111,-0.490248685934803,-0.0384655778262741,0.333889438518959,0.202937380713264,0.0985014985110573,0.470830559542396,0.20402472872281,0.281021639874914,0.198632162742518,0.246604577397413,0.0353312768770485,0.0744242411147501,0.120078933472747,0.186904720241133,-0.00495229763388459,-0.0389393261105942,0.0220669639700323,0.00154870311602997,-0.00868163744428188,-0.0284898738362031,-0.0186194785719662,0.107276121083695,-0.103632990157369,-0.0416739014474962,0.0139265925293678,0.0346320730496801,0.035046441646972,0.103371413638081,-0.0822855087245652,-0.0778996099351353,0.031670717005086,0.0726043417818641,0.100615243935753,-0.00256718978650125,0.0168137656928647,0.0517897337401938,-0.0218801684841591,-0.035634711566135,0.036693298074591,0.0105079778429993,-0.0102177627088967,-0.219455241401363,0.134623822880064,-0.0383409196178539,0.0326856595331419,-0.17408144272868,-0.187967882905144,-0.0106188152969236,-0.0613465223792958,0.110817016971726,0.16005945408355,-0.0637186472982317,-0.122342347024249,-0.0998173341733198,0.129441561501406,-0.071752424806706,-0.0722299309317572,-0.156454680592097,-0.104059034498752,-0.0324322320370311,-0.136256469238089,-0.0567939314242077,-0.035991642046431,0.0656083164793164,-0.0972852470329518,-0.0701347066909341,-0.147404702369035,-0.127679345253728,-0.658352497000943,1

dist_obj = as.dist(1 - cor_mat)
clust <- hclust(dist_obj, method = "complete") # do not use "ward.D2" here, because we use correlation distance
clust <-
  seriation:::reorder.hclust(clust, dist = dist_obj, method = "OLO")
data.table::setkey(column_groups, column)
anno_df <- as.data.frame(column_groups[, "group", with = FALSE], row.names = column_groups[, column])
rownames(anno_df)[rownames(anno_df) == "Sex"] <- "Sex (f)"
anno_df$group <- tools::toTitleCase(as.character(anno_df$group))
my_heatmap <- pheatmap(
  cor_mat,
  cluster_rows = clust,
  treeheight_col = 0,
  cluster_cols = clust,
  annotation_row = anno_df[clust$labels[clust$order], , drop = FALSE],
  # annotation_row = anno_df[clust$labels[clust$order], , drop = FALSE],
  color = colorRampPalette(rev(
    RColorBrewer::brewer.pal(n = 7, name = "RdBu")
  ))(100), 
  silent = TRUE
)
pdf(file.path(fig_dir, paste0(
  "correlation_heatmap_", cor_method, ".pdf"
)), width = 19, height = 14)
grid::grid.newpage()
grid::grid.draw(my_heatmap$gtable)
dev.off()

## png 
##   2

grid::grid.newpage()
grid::grid.draw(my_heatmap$gtable)